I went to Sousse last year on a late deal to Tunisia, so I won't be able to comment on Hammamet, but did take one of the overnight trips around the country.
I would highly recommend one of the tours that encompass El Jem, Matmata, Sahara... the country is amazing to visit and some spectaculur sceneray, usually pointed out by the tour guide with words like 'as seen in Indiana Jones / English Patient / Star Wars / Gladiator...'
If you decide to go on the tour there are a few things I would recommend bringing... Firstly bring some babywipes, they do recommend bringing toilet paper, but for some of the sites you visit there are no hand basins so baby wipes double up for hand sanitisers.
A small torch, most tours give you a very early wake up call to see the sun rise over the salt flats, if you have stayed near the sahara the night before you have 1-2 hour drive there... the facilities there don't have any lights... and you will be drinking a lot of water as you travel around, so you will use the facilities as most locations! At the stop we used the toilets didn't have a toilet either, just a hole in the ground, so both the the wipes and torch were much appreciated!
Bring plenty of water, at most of the stops you can pick up bottles of water, but some of them do charge 2 or 3 times what you pay in the supermarket close to your hotel.
Bring a warm top, although it will be very hot the bus is air conditioned and it can get very cool, also that early morning start is pretty chilly.
A book or 2 can also be useful, as the 2 day tour we did was 1300km, so there is a lot of sitting on a bus going from A to B.
Be aware that although most things are included in the cost of the tour, most of the guides will still ask you to pay for stuff... Some people give in and pay to avoid arguements, others just refused, there didn't seem to be any hard feelings either way.
Its suggested that you bring a small backpack, however you can leave a suitcase in the bus luggage area, so just a small backpack with the stuff you'll need on the bus and pack your overnight stuff into a second larger bag.
Enjoy it.