There is accomodation to be found all over Lamu. Some People stay on Lamu Island itself. You'll find a number of visitors in Shela town. Especially at the popular Peponi Hotel. Directly across from Shela are the residences on the quieter Manda Island, the stand out one being the Majlis Hotel
Shela

Shela, Kenya

Shela is one of the 4 Big "Villages" on Lamu Island. It has the highest density of hotels and vacation rentals. It also has several villas belonging to various international celebrities ... and many if not most of them are available for your stay. Check out listings on Airbnb.