Hey Moon,
We liked all the places we stayed at for different reasons, just like different islands. We always get a place with a kitchen (on a low budget) and a pool is nice also. Mayan Princess was a good location in town, good price, good view from second floor balcony, nice rooms etc. but no pool, nice swimming although there are more piers out front now. We would stay there again if we could get over the pool thing.
Banyan Bay was kind of a splurge for us, must of been an anniversary or something. Very,very nice roomy two bedroom, jacuzzi (which we got busted in by the housekeeper the first morning there), pool, security, as if you needed it, etc. It was a ways south of town probably 20 minute walk.
Belizean Shores was well north of town, rooms ok, good views from second floor, nice grounds, great infinity pool, free kayaks and a mooring buoy at reef to tie up to. I liked this area away from everything, quiet, nice shaded beach walks, or riding bikes to town along beach (requires stops at palpapa bar).
I know it makes no sense but next time we would either stay in the middle of town where everythings happening or even further north of Belizean Shores up around Mexico Rocks where the water gets really purdie.