Hammamet is one of the oldest tourist centers in Tunisia. Roman Pupput stood here, the town takes its name from the Arabic for baths, and a small medina and a fort have stood at the water's edge for centuries. Then in the 1920s a Romanian millionaire, Georges Sebastian, built a villa here, and the artists, aristocrats and politicians followed. Paul Klee came in 1914 and was struck by the light. Yasmine Hammamet, the big resort next door, only came in the late 1990s, and it is a different place altogether.
So this is two trips in one, and the plan keeps them apart. The old town and the beach are small and easy, which is why a few days are enough for Hammamet itself. The rest of the time goes to the Cap Bon peninsula around it: Nabeul with its pottery and Friday market, the fort at Kelibia, the Punic city of Kerkouane (UNESCO) and the Roman quarries at El Haouaria. Cap Bon is green, close to Tunis and far less visited than the resort strip, and it is the reason to give Hammamet five days rather than a weekend.
Day one is the medina, the kasbah and Dar Sebastien, day two is Yasmine and the beaches, day three is Nabeul, day four is the long drive to the tip of the peninsula, and day five is slow. Start on a Wednesday: that puts Nabeul on a Friday, when its big weekly market runs, and the Kerkouane museum, which is closed on Mondays, on a Saturday. For the country as a whole see Tunisia. If you want the capital and Carthage first, our 5 Days in Tunis guide is an hour away, and 5 Days in Sousse covers the coast to the south.