We always used to go for a wander around the small harbour/marina after breakfast and while away some time in some of the little cafe bars and have lunch at what was known as the "five dinar" restaurant.
Hop on the mini-train into Sousse for a nosey around the souk (bazaar) and take a quick gander in the fixed price shop to give you an idea of the maximum price you should pay before you start haggling in the bazaar.
Since we've been I hear there's a few more bars in PEK now and there was a micro brewery had opened when we were there last and I gather a nice fountain area near where the Maison des Jardins apartments are situated just by the shops.
We also took the 2 day safari but that was the first time in Tunisia when we were in Hammamet.
There's loads of places to go and if you're feeling adventurous - jump aboard the train in Sousse and explore.
We've mostly gone late summer and mid December so can't help too much with temperatures but it will be hot and dry in June. We've never done AI in Tunisia as we like to get out and about.