If you are thinking of going to Eleuthera (and of course you want to come to this beautiful island), then take a look at
Tropical Dreams. They have suites, efficiencies, and a two bedroom apartment.
There are lots of vacation properties for rent on the island, but they can be very expensive. Tropical dreams is very reasonably priced and has everything. It's very central. You can walk to both oceans, or rent a car and tour the whole island from here. The store is 5 minutes walk away. I loved being so close to a local settlement.