Yam's: Great cafe
Yam's is a typical Tunisian cafe opposite the Monoprix supermarket near Carthage Dermech station. After I finished spending the day walking around the sights, I came here and sat outside for a rest, cup of good coffee and a fantastic chocolate and banana crepe, which I highly recommend having.
Baguette: Near Carthage Dermech station
One of only a few places to get any food in Carthage, Baguette is a fast food burger restaurant that is similar to a McDonalds or Burger King with similar food and decor. It's located near the Monoprix supermarket near Carthage Dermech station. It's a good idea to get food either in here or in the supermarket before you set off around the sights.
Picnic Lunch in Carthage
There aren't very many restaurants in Carthage and those that are found there tend to be expensive. Hence, it makes sense to bring a picnic lunch, especially if you plan on seeing a lot of the ruins and if the weather is fine. Alternatively you could spend the morning in Carthage and take a train to nearby Sidi Bou Said for lunch.
We brought a picnic lunch (from the central market in Tunis) and had a lovely lunch in the Antonine Baths, one of Carthage's best known sights, down near the seafront.