Take a camel ride out of town to one of the Tuareg camps in the surrounding desert. It is the touristy thing to do, but it is genuinely fun -- the dunes outside Timbuktu are beautiful, especially at sunset. Before you go with anyone, make sure you are visiting a real campement and not just a carpet sales operation. Ask your hotel for a reliable guide.
Tuareg Camps
Camel rides to desert camps outside Timbuktu