As it happens years ago we went to El Kef from Tunis (via Dougga ruins) and El Kef is just 40km from your border post. I recall we used a combination of buses and 'shared taxis' (station wagons / mini buses). It was inexpensive and could be done in a day, even if you start from Hammamet as buses to El Kef are frequent.
From a resort like Hammamet I imagine you may be able to rent yourself a car, although I've never done that. The driving standards in rural Tunisia are not so bad but if you've not done it before it would be initially stressful.
Ch
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