Hammamet is well placed for exploring northern Tunisia. Louages (shared taxis) depart when full from the main station and are the cheapest option for most day trips; private taxis are faster and more convenient for groups.
Nabeul (20 km, 20 minutes) is the ceramics capital of Tunisia and worth a half-day trip for its Friday market, pottery workshops, and archaeological museum. The Roman remains and the market together make a good morning out.
Tunis (65 km, about 1 hour) offers the Medina, the Bardo Museum with its extraordinary Roman mosaic collection, and the ruins of Carthage nearby. A day is the minimum; two would be better.
Dougga (130 km, about 2 hours) is the best-preserved Roman small town in North Africa and a UNESCO World Heritage Site. The Temple of Jupiter, the theatre, and the remarkable Capitol make it one of the finest Roman sites in the world. The journey requires a change in Testour or hiring a car, but it is worth it.