You're right, lots 'n lots of places.
One way to cut out some of the lodging choices is to decide where on the island you want to stay. North of the bridge, south of town, or "in town".
This link will being up a map, with click-able links to lodging.
I'd suggest "in town" or on the edges aka a short walk on the beach.
IMHO needing to hop in a boat or ride a golf cart to town, takes a lot of the spontaneous "events" (like going for ice cream) out of the equation.
Have a GREAT time!
"The truly happy person is the one who can enjoy the scenery even when he must take a detour" - Anonymous