I had exactly the same questions when I went to Nassau last August. I looked at the Sheraton, the Hilton, and Cabbage Beach. While Cabbage beach sounded nice, I wanted to swim and they warned that the water is a little rough and there's a pretty good drop off a little ways out. Sheraton was $40 for the pass, and the BCH was $20. We also looked at an excursion on Carnival for the all-inclusive resort on the island that was 5hrs long, and it included all food, drinks, and facilities. I also found out that you can get that same pass through the resort for only $50 and you get like 8hrs instead of 5, and it's cheaper than through Carnival.
We ended up going to the BCH. You just walk in, ask about a day pass, and it was $20 to use their private beach and pool. They give you towels, and there's a little stand to the side that rents snorkel gear for $5. FYI, their bar drinks are pricey though. I got a can of a local beer (Kalik) that cost $5. At least it was good beer. :D