I would suggest Hammamet/Nabeul, Mahdia or Monastir/Skanes. Hammamet has been attracting tourists since the 30's. The town that is, not Hammamet Yasmine which is a new development to the south of Hammamet. At the north end you run in into Nabeul which is a historic centre for pottery and ceramics. The medina in Hammamet is very small and can be a bit frantic. Intereting private museum with a collection of traditional wedding clothes. Also you not too far from Tunis or Sidi Bou Said and Carthage.

Further south and an easy airport transfer is Skanes. While I admit Skanes itself is a not a lot more than a great sandy beach and some hotels; it is very convenient for accessing Monastir or the city of Sousse. Taxis, louages(shared taxis), buses and trains are cheap and regular. Both have interesting musuems, markets, medinas and some film history. You must have seen life of Brian? El Jem with its coliseum is only a short trip away, as is Kairouan.

Mahdia is further south again and is a fairly small town which is now attracting tourists. Really it doesn't make that much diffference, it's easy to get around in Tunisia if you want. With a little one I would choose a short airport transfer and not go in high summer. It gets very hot.

Hi there, I will say a budget of 2k, is more than enough for a hol for you is well more than enough, (the 1st time me and son went to Tunisia 4years ago, I paid £1000 for the 2 of us, middle of August on a h.b.baisis, with me being only 1paying adult, I had to pay adult proce for son,) and also take into account, you may get a free child place. I also found it so cheap out there, for food and drinks, that if I am honest, for me personally, it would have been not worth me and son going A.I.
On the 3occasions we have been, I have always found different nationalities. Tunisia is a place you either love or hate, I find it a lot more relaxed holiday destination, have not onece seen larger louts, (soz to any larger louts, ) all the people we have came across have always been very friendly and polite. We have stayed in Sousse twice, and recently stayed in Hammemet, Sousse, I found was lively that Hammamet, but it was a nice lively, if that makes sense, Hammamet, I found was a lot more relaxing, the hotels we have stayed in, the beaches have been on the doorstep of the hotel, which I found is a huge advantage being a beachy gal The transfer time to Hammamet was a good 1hr 45 mins to 2 hours away, were with Sousse, if memory serves me right, was only about 30 mins to 45 at the most. I found it easier to get out and about a lot more in Sousse, although, both places appealed to me.
Hope this is of a little help