A small but good museum on the outskirts of the city located in Education City. It has a good collection of modern art that includes many regional artists. Frequently has traveling exhibitions. It can be difficult to find in the ever changing construction in Education City. There is a bus from the Museum of Islamic Art so you could always go there and save yourself the driving headache.
I'd give this five stars, but it's a hike from the center of Doha--although as a sort of bonus, you get to go to the very space-age-mars-colony-feeling Education City, which is a bit bizarre. The museum has an interesting permanent collection, but often that's not on view because the whole space is dedicated to some special show. I saw a Cai Guo-Qiang exhibit there that was beautiful, tailor-made for Qatar and really educational, in a good way. If you're curious about Doha's contemporary art efforts, this is a must-visit.