This was our third visit to Nassau, we walked the port area, went through the straw market, and did a horse carriage ride. Enjoyed the carriage ride for we saw parts of Nassau we had not seen before - little pricey though.
There will be plenty of taxi drivers waiting to greet you at the port, but the best thing you can do is get a map of San Juan in advance, research and pick what you want to see - for most likely you will only have a few hours in port. El Morro Fort is beautiful, the Raccies Fountain and City Gate are well worth the walk. We utilized the free trolley services in San Juan. My husband and I also did a horse carriage ride in San Juan - great way to see some sites without all the walking. Don't forget to stop at Don Q Rum Factory for a free sample of their rum.
Grab a taxi, negogiate your price before you board and your locations. The only negative I can say is we were not taken to Mountain Top, our taxi driver told us it was closed to his taxi service that day. But the taxi driver did a great job of showing us the island sites, dropped us off at Charlotte Amelia for shopping, then we grabbed another taxi back to port - $4.00 per person for taxi - and the tour was $25 per person - another great fine at St Thomas is the Butterfly Exhibit right in the port - great for kids to experience! Again do your research on-line before you go so you will know the sites you want to see for you will have little time in port.
Originally I had communicated with a tour operator and had plans - long story - those plans were changed in port - grab a taxi when you disembark - see this tiny island - won't take you long and will be well worth the $20 per person - the water is beautiful!