I'll arrive at Doha, Qatar (Hamad International) at 19:25 and I'll continue my trip at 02:55 so I'll have 7.5 hours at Doha. Is it worth to visit the city at night? What is the travel time to the city?
At peak rush hours (5pm-8pm), drive from airport to city center is 1+ hours, although the distance is only 15-20 kms.
At night, food and restaurants are open till about 10pm, and around midnight its all very silent except some five star hotel bars.
The major attraction you might want to visit will be Souq Waqif, translated as Traditional Market, situated on waterfront, and consists of numerous restaurants, spice markets and other handicrafts, but I doubt it also closes around 10-11 pm.
If you are from a developed country (Europe/America), and you want to come out to land-side, you need to get tourist visa, cost $100, payable by only any credit or debid card, no cash. If you are from Asia/Africa, you can not get tourist visa on arrival.
Taxis are available for about 50 Qar to and fro city center, one side.
Some malls are open till 1am. You aould also have a stroll at Corniche, just near Souq Waqif, the waterfront, about 5-6 kms, free of cost and all night without any worries. Although beware, there are almost none food stalls or shops or outlets there.