Nassau right by the port is abysmal. We took a carriage tour on recommendation of another cruiser, and it was bad. Most businesses were shut down, and the driver had nothing interesting to say. Fortunately, my son suggested going to the beach, so we took a cheap cab ($4/pp) to Cabbage Beach. Do it. It's an unusual, steep beach with rolling dunes and huge, powerful waves. We found a high spot and enjoyed the sun. There's a bar that sells all-you-can-drink rum drinks for $20, and the guy was very insistent that our 15yo daughter should buy one. "You're on vacation!" Uh, no thanks.
We went to Orient Bay beach in St. Martin, and got 2 chairs and an umbrella for $20 in front of Kakao restaurant. Our French/caribbean lunch there was AMAZING, but priced in euros, it wasn't cheap. Beach was gorgeous, with fine white sand and every shade of blue water. Taxi is $8/pp each way.
St. Thomas was way better than expected. The downtown area is filled with typical tourist shops, but most of the buildings are 300+ years old. Very cool cobblestone streets and ancient brick structures. A guide on the street sold us on his open air bus tour of the island for $25/pp, taking us to a couple picturesque lookout points, giving some history, and spending 2 hours at Secret Harbor beach, which was delightful.