What is near cruise port
The port is called La Goulette, and there is a small beach close to the terminal, but for a better beach you should head a few kilometres north to La Marsa, a seaside suburb with a few beachside hotels. To get there, take the TGM train from La Goulette north to either La Corniche or Marsa Plage stations.
However these are not the best beaches in Tunisia, and it would also be a shame to spend a day at one of these beaches and miss out on what the city has to offer, especially if you haven't been there before. By taking the train in the other direction, the city centre is very close to the port and has a fascinating old city (medina). Alternatively, if you wanted to spend a little time on the beach, you could combine it with a visit to Sidi Bou Said, a beautiful blue and white village on the clifftops with spectacular views over the bay, and/or the ruins of Carthage, both of which have stations on the trainline to La Marsa.
We didn't go for the beaches but they sure look beautiful. I could see a broad white beach directly below Sidi Bou Said from the village which looked like it stretched all the way to Carthage. There are also some gorgeous looking beaches south of Tunis. Not much help, I know.