Hotels and alternatives
Quite little in Carthage itself. The hotels you find right here are rather expensive, and you might like to consider rather staying in La Marsa (5 km) or Tunis (17 km). Among the hotels here, the Résidence Carthage offers best value for money.
Restaurants and alternatives
Beyond the hotels, there are no great places to eat in Carthage. Good alternatives are Sidi Bou Said (2 km) or Goulette (6 km).
Nothing, except in the hotels. Tunis is your best chance, and even that is not terribly great.
Do this in Tunis.
Use the local train. This is great also for moving around the sites of Carthage. There are 6 stops along the railway for different parts of old Carthage.
Carthage Salammbo and Carthage Byrsa will take you to the Punic port, the Tophet, Hippodrome and the Paleo-Christian Museum.
Dermech is good for the 1890's Cathedral and the excavations.
Carthage Hannibal is good for the Antonine Baths, Archeological Garden, Theatre and 'Building with Columns'.
Carthage Presidential is good for Damous el Karita, the largest ancient church in North Africa.
Carthage Amilcar is good for Basilica St. Cyprian and Basilica Majorum.