Itinerary feedback for trip in May

My wife and I are considering the following itinerary for our trip to Tunisia in May. Open to any feedback, but largely curious if the logistics of getting to and from Tozeur, as well as visiting el gem from Tunis vs. from Tozeur is the best logistical approach?

Itinerary: Arrive in Tunis Fly to Tozeur Spend a few days exploring Tozeur and Douz Fly back to Tunis Take a day trip to visit El Jem And spend our time in Tunis visiting neighboring Carthage/Sidi Bou Said