I would recommend looking at the central business district for lots of 4* hotel bargins (in particular if you are going for a weekend). Lots of great hotels right on the other side of Canal Street, seem to get better deals there.
In the FQ, some old hotels might not have a pool. I would be shocked if any in the Central Business District didn't have one (some even have pretty cool rooftop ones).
By the way, welcome to Flyertalk!