On our very first trip to Nassau (non-cruise), we stayed at the Marriott Crystal Palace Resort and Casino located, I believe, on the Cable Beach area which has several resorts/hotels.
This is not very close to where the ships dock. You will need to take a taxi there and back. It was a few years ago and I don't recall the price of the taxi.
We really enjoyed our stay there but we were STAYING there. I don't think this will work well with your day in port but that is just my opinion.