Astronomy

There are many reasons to combine travelling with a look upwards. Given that you can see a different set of stars in the sky depending on the latitude you are at, if you're at all interested in astronomy and happen to travel across the Equator or even to the tropics, do take a look upwards at nighttime. More enthusiastic astronomers may even make a trip, in order to e.g. see a specific total solar eclipse that isn't visible where they live.
In modern cities, light pollution means that the starry sky is hardly visible. The far-off countryside provides an astounding view of the stars. Mountains and deserts are also better places to look at the stars than others, firstly because they usually lack the light pollution of modern civilization and secondly because air and all that's in it (primarily water) obstructs the clear view of the stars. If you are at 4,000 meters altitude, you already have a lot of the air below you. And a cloudy day is unlikelier in the Sahara than in say Oslo, making high desert areas ideal for observation of the sky, resulting in many observatories being in such places. And it should thus come as no surprise that the Atacama desert in South America which is both very dry and has high altitudes is a popular place for serious government funded observatories.
Also, astronomy is among the few sciences in which amateur scientists regularly make discoveries on their own, given that nobody can watch all the sky all the time and just having a good enough piece of equipment and looking at the right place by chance, you may discover your "own" comet, asteroid or other object.

Astrology

Astrology is the superstitious belief that astronomic events interact with human life on Earth. Though dismissed by modern science, astronomy and astrology used to be the same thing in ancient times, and astrology provides a historical background to today's knowledge. While western astrology is loosely based on Graeco-Roman mythology, there are other traditions of astrology in places such as China.

Not much equipment is needed to get started with amateur astronomy. A good pair of binoculars, or even just a good pair of eyes, can get you off to a good start. However, don't look directly at solar eclipses, even full ones.
Also, consider when visiting professional observatories that large lenses or mirrors are very sensitive to temperature and thus the observatories are usually not heated.

• Solar eclipses might be the most spectacular phenomenon visible from Earth's surface. By a lucky coincidence, the moon is barely large enough to cover the sun. Note that looking directly at the sun can cause eye damage or blindness so always take adequate safety precautions e.g. NASA's Eye Safety During Solar Eclipses or How to View a Solar Eclipse Without Damaging Your Eyes.
• Lunar eclipses, in which the earth is directly in between the sun and the moon, are visible from any point on Earth where the moon can be seen. In a partial lunar eclipse, you can see the earth's shadow on the moon, and in a total lunar eclipse, the moon looks red (sometimes known as a "blood moon"). You don't need eye protection to look at it (because you're not looking at the sun). NASA provides tables of past and future lunar eclipses.
• Midnight sun
• Northern Lights and Southern Lights are usually only visible at latitudes far from the equator.
• Meteors are seasonally visible.
• Comets can be observed occasionally by amateur astronomers without any specialized equipment.
• Planets can be observed some months.
• The International Space Station (ISS) and Iridium flares can be observed almost daily. Web sites can tell you when and where to see these, e.g. NASA's Space Station Sighting Predictions and Iridium Flare Predictions. Predictions are based on your location so make sure you have told the site where you are!
• Stars and constellations.
• The Milky Way may be viewed in locations not subject to light pollution (see below).

Light Pollution

Whilst objects like the Sun and Moon are bright (they are close to us), many astronomical objects are harder to see. Our modern lifestyle has resulted in many areas having street lighting and this night time illumination interferes with seeing many smaller dimmer objects in the night sky. And the impact of this lighting is dramatic; in a totally dark skies most people will be able to see more than 4,000 stars with their naked eye, but in a typical suburban area that number might reduce to 450 and move to a city and the number drops still further to 35.
So to see most, find a dark location. Earth monitoring satellites have allowed scientists to create light pollution maps which can help find the best places to watch the night sky; for example Dark Site Finder Light Pollution Map.

Adaption to the dark

When we move from light to darkness our eyes gradually adapt to be more sensitive. There's two stages, a fast adaptation in a couple of minutes then a longer process which varies between individuals (e.g. with age) but which can take 30–45 minutes. If you are watching the night sky meantime, more and more objects appear. You need to stay in darkness to preserve your night vision, look away and cover your eyes immediately if there is a car headlight or someone waves a torch. The difference between non adapted and fully dark adapted is "dramatic" in a dark area.

Averted vision

Our eyes use two different types of cell to detect light: rods and cones. Cone cells provide colour vision, are concentrated in the centre of focus of the retina, and are not particularly light sensitive. Rod cells are far more light sensitive but cannot distinguish colours and are on the periphery of the retina. So to see the fainter objects in the night sky the trick is to use averted vision: don't look directly but slightly to one side, so the light from the faint object falls on the more sensitive rods. It is better to have the target nose-side of your gaze, as there is a blind spot around 15° to the temporal side. This is a difficult technique to master – the usual beginner's mistake is, on spotting the object by averted vision, to instinctively gaze directly – so it disappears! But with practice, you can pick out objects 20–40 times dimmer than by looking directly.

Astronomy can be used for navigation, and was an important skill for seafarers until radio based systems and later satellite navigation became reliable and affordable (Gee, Loran and Decca were developed in the 1940s, Loran-c became widespread in the 1970s, GPS in the 1990s). Celestial navigation is still taught on many advanced navigation courses, and usable at least as a backup when electronics fail (and in terrible radio weather and other special conditions).
Before the chronometer (constructed in the 18th century), several celestial events were suggested for establishing the time and thus the longitude, such as eclipses of Jupiter's moons. The latitude is more easy to get, from the angle above the horizon of the sun at noon and of stars late in the evening and early in the morning (the horizon has to be visible). As one degree means a hundred kilometres, equipment is needed; the Polynesians used holes drilled through coconut shells.
On land, an approximate course can be kept by observing the sun, moon and stars (see Orienteering). For example, the sun is due south at noon (1 PM if daylight-saving is in effect) in the northern hemisphere and it will swing west by 15 degrees every hour. This enables rough-and-ready reality-checks in a strange city: say it's 4 PM and the sun's on your right shoulder then you're heading sort-of south-east, towards the bottom right hand corner of your streetmap, is that what you intended? If you need anything more precise, you need to account for how your time zone relates to your position (this means an additional hour off in Brest, or elimination of the DST effect in Kirkenes).

As you travel about the world, the night sky can vary significantly. However, north-south travel is by far more important for astronomy than east-west travel. If at noontime, you could see the midnight sky halfway around the world at the same latitude, it would be only be half the difference between last night and tonight. (Which to the casual observer isn't very much.) There are a few exceptions for events of short duration, such as an eclipse.

On the other hand, every star visible at the North Pole will be invisible at the South Pole, and vice versa. The poles are also the only places on earth where no star ever rises or sets. For everywhere else (except the equator), stars can be classified into three categories at any given latitude: "never risen," "sometimes risen," and "always risen." "Never risen" stars are those over 90 degrees from your latitude. You need to be closer to the equator to view them. "Sometimes risen" stars rise and set according the seasons. They appear or disappear over the horizon nightly, and have periods where can't be seen, as they're only risen in the daytime. "Always risen" stars are based on how close to the poles you are. For example, at 80 degrees north, every star is "always risen" except those between 10 degrees north and 10 degrees south. At 70 degrees north, it becomes 20N and 20S, and so on. At the equator, all the stars are "sometimes risen" (90N and 90S). If you're planning an extended trip near the equator, it takes about three to six months to view all the visible stars (depending on if you're willing to get up before dawn).
Example: You live in the temperate zone in the Northern Hemisphere and want to view the southern constellation Hydrus. It's southernmost star is just above 78 degrees south. Using the 90 degree rule, 90 - 78 = 12. So, anywhere much above 12 degrees north, the star won't ever be visible. However, viewing it at this latitude is not very likely, as it could easily be obscured by hills or buildings right at the horizon. In addition, the star won't be risen at night for months at a time. At 12 degrees south or further, it would be much more easily viewed, and risen every night of the year (local conditions permitting). You'd have to be in Antarctica for Hydrus to be directly above in the sky, though.

Pre-modern observatories are usually obsolete today, and remain as museums, or sites of education. As light pollution in their heyday was not the kind of problem it is today, they are usually located in cities or at campuses, easier to reach than those built in modern times.
Most modern research telescopes are enormous facilities in remote areas with favorable atmospheric conditions.

Europe

• European Space Agency's Columbus Control Centre

  phone: +49 8153 28-2711
  address: Münchener Straße 20,82234 Weßling
  is used to control the Columbus research laboratory of the International Space Station, as well as a ground control centre for the Galileo satellite navigation system. It is located at a large research facility of the German Aerospace Centre. (DLR). German registration form
• Stjerneborg observatory, Hven Island, Sweden - Tycho Brahe's observatory.

• University Observatory Vienna

  address: Türkenschanzstraße 17, Währing, Wien, Austria
  The Institute of Astronomy is part of the University of Vienna, located inside a fabulous historic building. The building and the Sternwartepark were closed for visitors up until recently. The park contains many rare trees. It has a mini observatory on the roof. Guided tours are available.

• The Royal Observatory

  phone: +44 131 668-8100
  address: Blackford Hill, South Edinburgh, United Kingdom
  Take a tour of the dome, housing one of Europe's largest telescopes. Learn about the history of the observatory and some of the cutting edge work they are carrying out today. If the weather is clear you can observe the stars in winter or the sun (through a special telescope) in summer. On some Fridays there is a special theme - check website for details.

North America

• Mt Graham International Observatory

  phone: +1 928-428-6260
  address: 1651 W Discovery Park Blvd, Safford, AZ
  Operated by the University of Arizona and situated in the Pinaleño Mountains west of Safford, this observatory offers periodic tours for the public. Reservations required, preferably two or more weeks in advance. Tours depart from the Discovery Park Campus in Safford.

• Kitt Peak National Observatory

  phone: +1 520-318-8726
  address: Tohono O'Odham Reservation, AZ
  Operates several astronomical telescopes plus a large solar telescope. Several guided tours are available, as well as a nightly observation program (reservations required).

• Mauna Kea Observatories

  phone: +1 808-961-2180
  address: No street address
  The observatories at the peak of Mauna Kea itself are off limits to anyone who has no 4-wheel drive vehicle and has not gotten permission to visit, though groups of more than 10 may make a special request at least a month in advance. However, there is a Visitor Information Station at an altitude of 9,200 feet (2,800 meters), where the local Astronomical Society assembles very good portable telescopes every night and shares them and their knowledge with visitors for free. That altitude is better for the naked eye than the peak, anyway, because at higher altitudes, the lack of oxygen starts to decrease people's ability to see. The sky at Mauna Kea is unparalleled: There is an extremely low level of light pollution at Mauna Kea because it is high up and far from cities, and also because the cities and towns on the Big Island of Hawaii use low-pressure sodium street lamps and some LED lamps with very low blue light emissions, rather than more common, light-polluting types.

• McDonald Observatory

  address: outside of Fort Davis, Texas

• Fred Lawrence Whipple Observatory

  phone: +1 520-879-4407
  address: 670 Mt Hopkins Rd, Amado, Arizona
  Call ahead for tour information.

• Adler Planetarium

  phone: +1 312-922-7827
  address: 1300 S. Lake Shore Drive, Chicago, Illinois
  The first museum dedicated to astronomy and astrophysics in the United States. Also has a telescope that the public can access for viewing of celestial objects on special occasions.

• Dearborn Observatory

  phone: +1 847-491-7650
  address: 2131 Tech Dr, Evanston, Illinois
  Observatory of Northwestern University, open to the public once a week. Reservations highly recommended.

South America

While the headquarters of the European Southern Observatory are in Garching near Munich, Germany, the observatories are located in northern Chile.
These include the:

• European Southern Observatory

• New Technology Telescope, La Silla, Chile
• Very Large Telescope, Paranal, Chile
• Atacama Large Millimeter/submillimeter Array, Llano de Chajnantor, Chile
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  Atacama Large Millimeter/submillimeter Array Public VisitsRegister for a pass in advance. No children under 4. ID required

The climate and geography in the Atacama Desert, Chile make it a great place for night sky observing; dry air and more than 300 lear nights each year. In addition to the professional research telescopes, astronomy enthusiasts can take advantage of the conditions at SPACE a specialist Astronomy tourism company and resort

• San Pedro de Atacama Celestial Explorations

  phone: +56 (55) 2 566 278
  address: Caracoles 166, San Pedro de Atacama, Chile

• Science tourism
• Space