Ibusuki

It styles itself as a sort of "Hawaii of Japan," and does exude a peaceful atmosphere. It is famous for its flowery botanical garden, proximity to the tranquil Lake Ikeda (池田湖) and the green conical Mount Kaimon (開聞岳), and a small island with a disappearing sand walkway called Chiringashima (知林ヶ島). Yet it's the natural hot springs beneath the beach called sunamushi (砂蒸し), roughly translated as a sand bath, that is the town's biggest claim to fame. If you're daring or curious enough to try being buried in steaming hot sand as a kind of luxury spa experience, you'll find a most interesting chance here.

Getting to Ibusuki will almost certainly involve going through Kagoshima.

By plane

The nearest airport is Kagoshima, which is 1 hour 30 minutes away by car.
Kagoshima Kōtsū run 8 buses a day to Ibusuki and Yamagawa, taking 1 hour 35 minutes to Ibusuki Station (1 hour 50 minutes to Yamakawa Pier) and costing ¥2450. Otherwise, take a bus to Kagoshima-Chūō Station and take the train from there.
Rail Pass users may wish to avoid taking the bus all the way to Ibusuki, as you can go most of the way on the train instead. If you really want to make the most of your Rail Pass, you can take a bus to Kajiki, Hayato, or Kokubu Stations and take the train from there, though this option will require a change at Kagoshima-Chūō.

By train

Ibusuki is on the Ibusuki Makurazaki Line, which follows the east coast of the Satsuma Peninsula along Kagoshima Bay.
There is usually one local train per hour from Kagoshima-Chūō to Ibusuki (with many continuing to Yamakawa), taking about 1 hour 10 minutes and costing ¥1000. There are 3 Rapid Nanohana trains a day which take about 1 hour, and 3 Ibusuki-no-Tamatebako (or Ibutama for short) Limited Express trains which take 55 minutes and cost ¥2140.
Note that many local trains stop short of Ibusuki (at Jigenji, Goino, or Kiire), and that while IC Cards (Sugoca, Suica, Icoca etc.) can be used around Kagoshima they cannot be used as far as Ibusuki.
Trains are covered by the Japan Rail Pass and JR Kyūshū's All Kyūshū Area Pass and Southern Kyūshū Area Pass.

By bus

Kagoshima Kōtsū runs 6 buses a day from Kagoshima to Ibusuki and Yamakawa, but these take a hefty 1 hour 40 minutes, and at ¥950 are only slightly cheaper than the train.

By ferry

Although you are unlikely to use it, mention should be made of the ferry to Nejime on the Ōsumi Peninsula, which can be used as a shortcut to places such as Kanoya. There are two different services from two different terminals:

• Normal ferries run 4 times a day from Yamagawa port (30 minutes walk or 5 minutes drive from Yamakawa Station), taking 50 minutes and costing at least ¥700.
• High-speed ferries run 3 times a day from Ibusuki port (15 minutes walk northeast of Ibusuki Station), taking 20 minutes and costing ¥1000.

Cars and motorbikes are only carried on the normal ferries.

Chiringashima is a small, uninhabited island with a sand walkway that appears at low tide. From March to October, a sandbar of about 800 m allows you to walk across part of Kinko Bay to the island in about 20 minutes. The longest time the walkway appears for is four hours. According to city statistics, the walkway appears for over an hour 190 days a year, and 86 days a year it appears for more than two hours. The island is 3 km around and 90 meters tall at its highest point.
This sandbar is occasionally washed away after typhoons and disappears for a while, but it is restored when sands are brought back by the tide. The plant Vincetoxicum austrokiusianum, which is listed as an endangered species in Red data book, has been found on Chiringashima. On the island, there are esplanades and an observation deck. This island is known as a matchmaking spot for couples. Fishing or gathering shellfish is possible.
Ibusuki's botanical garden.

Climbing Kaimon-dake (開聞岳), or Mt. Kaimon makes for an incredible view on a clear day. From the very flat land and lake below, to the smoking Sakurajima to the north, to the peaks of Yakushima in the ocean to the south, there is plenty to be seen. There's no better follow up to the 4 to 6 hour hike than a day in Ibusuki's hot springs resorts. You can access the trail head by bus (you'll want to get of at Tozan Iriguchi (登山入り口)), or alternatively, by a very short walk from Kaimon's train station, which is nothing more than a platform and bench that can be reached after a short train ride from Ibusuki's train station.
The "sand bath" and related spas.

"Nagashi somen" (流し素麺)　is a fun experience of a meal in the warm weather, and involves grabbing swirling noodles from a small circular stream of water at your table.