Welcome to Big D.
If you want to stay very close to the airport, there is a Bone Daddy's BBQ in Grapevine. It is good food and the waitresses wear skimpy outfits. I dont recommend these types of places for the waitresses though, the food is actually quite good.
You seem like you may have enough time to get to actual Dallas though. In that case, check out Pecan Lodge in Deep Ellum. Then you have to go see where JFK was shot, since that is what everyone seems to do except the locals. (I have only driven by a few thousand times)
Dallas, like all of Texas, is a driving city. Uber and cabs are not cheap and most people rent cars. Just keep that in mind since DFW is not a quick rental car turn around.
Now, if you are in Love Field, well, that is a horse of a different color. Much smaller and easier to deal with, but also much closer in, so no problem there.