The only hotel of the island is Halki Palace. Still in the town's limits but away from the centre. The only cars you'll find on the island are government vehicles. Prices are fixed and are on a red sign on the left side of the pedestrian entrance. You can use a horse drawn carriage as a taxi or take a tour.
Bicycles are fore hire as well.
The wooden building was constructed in 1911 and its four storeys are built around a kind of patio. The hotel is a distant mirror of the past for most of the furniture is still as it was. A pity is that maintenance is a bit behind schedule but when we were there works were in progress. Buyukada is mostly overcrowded thanks to its beaches and lot's of green. If you prefer calm environments you should visit one of the other islands.