I stayed at Palm Cay Marina at the southeast end of New Providence earlier this year. It is a large marina but the number of transient slips must not be too great because I could not get a slip at the end of January.
The amenities are good though the showers are a little strange; two showers in one room but both have doors or curtains. Must be unisex.
The marina is in a private gated community so security is high. The only problem is that you need a car to go anywhere. They have a loaner for 2 hours at a time that was not hard to get. This will get you to nearby markets (not too good) or to larger markets farther away. It will even get you to the two marine stores in Nassau that are only a block apart. But the loaner car will not give you time to explore. I rented a car for one day through the marina to pick people at airport and do other things.
I ended up at Nassau Yacht Haven at the end of January because I was not eligible to get into the Nassau Yacht Club (need to belong to reciprocal yacht club). It is very reasonable for long term which I needed and the amenities are good (unless you are very picky). It is across street from the two marine stores, walking distance to upscale market, and long but reasonable walk to downtown. Can also walk to Paradise Island.