For moderately-priced Arabic food, I like Assaha Lebanese Village, on airport road, or Al Khaimah on Al Saad Street. Turkey Central has possibly the best kebabs in town, as well as good mezze and shawarma, at bargain-basement prices. Al Sayyad, at the Diplomatic Club, is also good but slightly pricier. Al Shami Home Restaurant (C Ring Road branch) is decent but with a nice environment. Khan Farouk, an Egyptian restaurant at Katara Cultural Village, is pretty good and an attractive setting, including a lady making bread in the dining room.
As for Indian, Bukhara is a pretty good moderate one; or Swagath (branches in Najma or on A Ring Road), a lower-end choice with very good food; Asha's at the Villagio mall; or Chingari (pricier) at the Ramada hotel old tower. Shebastan Palace is a good Iranian (though pricier) or Shater Abbas (Salwa Road) is another choice.
As for nightlife, there isn't much. The only alcohol available is at upscale hotels. Decent lounges include Wahm (W hotel), Spice Market (also W), Skyview (La Cigale), Dunes (Grand Hyatt), Jazz Club (Oryx Rotana), Admiral's Club (Ritz-Carlton), or lounge at the Kempinski residences. The best cigar bar is the Library Lounge (Four Seasons); other nice ones, which offer outdoor seating, are at the Ritz-Carlton or Sharq Village. The Belgian Cafe (InterContinental) is probably the best pub/bar in town and Champions (Renaissance) the best sports bar. I also like the Manhattan Bar (Ramada new tower), a tiny place with a bit of character. As for night clubs, they are poor, but Crystal Lounge (W) is the best, followed by Pearl (Marriott). A few other hotels have night clubs, including La Cigale and the Ramada old tower.
A non-alcoholic version of nightlife can be found at Souq Waqif, probably the best tourist attraction in Qatar (though the restaurants aren't very good; Damasca is a semi-decent Arabic option), or the aforementioned Katara. The Pearl is the best spot for upscale restaurants and bars, but they have suspended alcohol service for the past six months.