If you take the north exit out of DFW, there are lots of places in Grapevine.

Take 114 west (coming out of the north exit there is a loop to the right pretty quick)

Exit Main street, they are on your right
- High End - Bob's Steak and Chop House
- Wood Fired Pizza - Fireside Pies

Exit William D Tate
Chains:
-- on your right of the service road all together
- Uncle Julio's (Tex Mex)
- La Madelin
- PF Chang's
- Chilli's
-- turn left at the light, cross the overpass and turn left again onto the service road all these are together on the right
- California Pizza Kitchen
- Boston Market
- Red Robin (Burgers)
- Carrabba's (Italian)
- Boston's
- TGI Friday's
- Outback
- Hooter's
-- on your right after crossing the overpass.
- Bone Daddy's (Hooter's of BBQ)

There is more stuff near by, but that gives you an idea if you want to leave the airport.

Irving is another option if you want to drive a little further.