What are you looking for? Restaurants that serve alcohol? Or restaurants then bars?
For food:
McAlister's deli is pretty decent food (no alcohol though), generally quiet. It is a "chain" restaurant, in that there are locations all over the midwest. Meals are around $10-$12
Abelardo's, lots of locations, pretty cheap, pretty authentic Mexican, but no alcohol.
There are a few good sushi joints, Tokyo sushi is the best (yes alcohol).
Le Bouillon: real good french food, very authentic. A little on the pricey side, but fairly expensive ($15-25 a plate, yes alcohol, mostly wine, some drinks. If you go, ask about the punch for the day).
Texas Roadhouse: Yes, it's a chain, but pretty decent steaks. Also Johnny's Cafe, although they are a hair on the pricey side (15-25 a plate).
Gerda's German Restaurant: Supposedly pretty good German food, never been there myself.
Also, buffalo company, it might be a bit busy, as it's next to a few bars, but is hands down the best buffalo chicken sandwich you will ever have. Also serves alcohol.
Oh, and John's Gyros, in Bellevue. Rated best of Omaha for like 3 years running. Super quiet place, doesn't serve alcohol. But you also get the added benefit of saying hi to an arfcommer (I work in the same building)