I'd suggest one of the condotels or suites places within walking distance of town. Among these are:
The Palms, 1 and 2 bedroom condo units at the south edge of town, pool, on water
Paradise Villas, condos at the north end of town, on the water, pool (note that you can reserve a unit here from several different sources, Tradewinds being one of them)
Mayan Princess, 1 bedroom condos, on water in the middle of town, no pool,
Caribbean Villas, rooms, suites and apartments in a lush tropical setting, on water, no pool, south of town but within walking distance
Belizean Reef Suites, condo units at south end of town, no pool, on water
Belize Yacht Club, timeshare/condotel about one-third mile south of town, pool, on water but there's a seawall
--Lan Sluder