Tunis’ must see attractions is the Bardo Museum: partly for the collection and partly because it is located in a marvellous 13th Century Ottoman palace. The museum itself covers the entire history of Tunisia: that is a lot to take in so allow a full day.
The Souk in Tunis feels a lot less touristy than those in some North African towns and cities; it is a vibrant place where people live and work. Because of this and because people are primarily interested in going about their business they will not bother you as a tourist.
A great attraction is the Zitouna Mosque, not only is it Tunisia’s largest, it dates from the 8th century. Although non-Muslims are not permitted into the Mosque you can visit the courtyard and take it much of the architecture including the distinctive minaret, a 19th century addition.