The Bardo Museum has recently re-opened with a new extension for the Roman mosaics. These mosaics come from a number of sites across Tunisia and are of the highest quality, surpassing any mosaic I have seen in Europe, including Pompeii and Herculaneum. If you have any interest in Roman life I cannot recommend this highly enough.
When we visited in Sept 2012, large parts of the original museum/royal palace were still being refurbished, but we were able to visit them with one of the local guides who expect a reasonable tip. I would recommend this as worth it.
Older guides recommend visiting in the morning, and although the extension has air conditioning it was getting warmer as we left in the early afternoon, so in summer it is probably still worthwhile trying to visit in the morning.