The place we rented was north of the Phoenix but south of the cut. It was a yellow house called Casa Caracol. We had a big crew so I rented both the upstairs and downstairs which can be rented separately.
There is a little fruit market across from the Belize Yacht Club. We picked up some fresh fruit and some really good homemade salsa there.
I am a big fan of having a golf cart. You can walk all over but it is fun to explore up to the Palapa Bar north of town and gives you a lot more dining options.