DFW Airport area is nothing but feeeways, corporate campuses, light industrial, and frontage road strip malls. You won't find much beyond chains.
You'll find a BJs and Humperdinks within a short drive. Dallas Homebrew is on I35E. There is another shop called Dr Jekyll's out in Arlington, but I have neve been there.
Dallas is blowing up when it comes to beer, just not with brewpubs. If you want to go to brewery tasting rooms, the Design District would get you the most bang for your buck in one area. Community and Peticolas are two of my three favs in Dallas, and they are less than a five minute drive from one another.
I would recommend trying to get out and away from the airport. Brain dead brewing is the only non-chain brew pub that I know of. It's in Deep Ellum, maybe a 20min drive from the airport with minimal toll depending on where you are staying. You might be able to hop light rail out there as well.
If you want restaurants with large beer selections, Meddlesome Moth is good but very pricy and Flying Saucer is cheaper. Flying saucer gives AHA 25% off food, but check the menu for the individual location as the selection does vary.
If you keep to local craft centric bars, you will be mostly drinking Texas breweries. Larger chains will have some Texas beers.