Originally Posted by
mecabq
This is very good advice all around. You can go to one of the hotels (Sharq Village, a Ritz-Carlton property, is closest to the airport), but if you want to get a bit more of a local Doha experience, then I would suggest Souq Waqif. It's only a 15-minute drive from the airport, and you can wander and have something to eat. If you're there during the day, then the Museum of Islamic Art is worth a visit, and also close to the airport.
(Taxis are difficult to come by at these two locations, however, so best to arrange in advance like tegwj.)
As someone living in Doha for years, I feel sad that people think Souq Waqif as "a local Doha experience". It's just a partial reproduction of a souq, now occupied by many souless cafes and restaurants that attract tourists and expat who hang out at night.
The nightbourhoods near to the airport can show you really how local people live their daily lives, if you are really serious on exploring it.