Cap Bon
The Cap Bon tour is a loop around the peninsula north of Hammamet. You see the fort of Kelibia, the Punic town of Kerkouane, the sea caves of El Haouaria and the hot springs of Korbous. Pack a swimsuit, because there are two good places to swim.
Sousse and Monastir
Sousse is about 1 h 15 south, and once you are there the stops sit close together, so this full day has very little driving between sights. You walk the Sousse medina and its ribat, then see the Monastir ribat and the seafront. It works well as a first day, since it shows you Tunisia at an easy pace.
Zaghouan and Friguia Park
Zaghouan pairs the abandoned Berber village of Zriba Olia with the Roman Temple of Waters, the start of the aqueduct that once fed Carthage. Friguia Park, on the other hand, is a half day of giraffes, zebras and bird shows, about 30 minutes from Hammamet.