Oqaatsut

Oqaatsut (Greenlandic) or Rodebay (Danish) is a coastal village with 46 inhabitants as of 2010.

The local shipping line Diskoline provides regular services from Ilulissat to Oqaatsut, and further to Sarqaq, in summer months.
You can also charter a boat from Ilulissat.
The most beautiful is, of course, to hike to Oqaatsut. It is a beautiful, pleasant, track, takes some 5-7 hours. You can not get lost, just follow the coast line.

Beautiful short and long hikes.
During the season, the kayakers come from Ilulissat for a 4-5 hours tour at the southern bay of Oqaatsut, beautiful experience to kayak between the icebergs. You can also join them directly in Oqaatsut.

There is a typical Greenlandic food store. At most times, it is well stocked.

All in all, the food in Rodebay is pretty bad, but they serve a rare Greenlandic microbrew there (you must have cash on hand to pay for the beer, oddly).
There is restaurant (H37), in a building of the earlier fish factory. It was run by a German couple, taken over by a nice Greenlandic couple in 2015. Excellent food.

There is a small, cozy hotel (Hotel Nordlys) with at least 4 rooms, clean, including breakfast, and a kind of a youth hostel, next to H37. I understand, there is even another bed & breakfast (as of 2017). The first and third can be booked through Booking.com.

Beware the mosquitoes if you're there in the summer. In early July, the mosquitoes are brutal — you will have to wear headnets 24/7 whenever you are outside.
In some years, there are no mosquitoes at all.