Yes, people do run round town. You see the football team running in Parc Belvedere, and there are a few single women who run there. My wife chooses only to run there with another female friend. There are quite a few places further out as well, depends where you live...
Cycling works well too, assuming you're ready for a bit of competition for road space. Its more do-able in the hot weather too. There aren't a lot of women that cycle in Tunis, but there are some.