We lived north of Dallas for many years and stayed at the airport as well as the surrounding areas.
There's the Grand Hyatt (new and at the international terminal) and then there's the "regular" Hyatt that is cheaper. It's at the airport as well and has free pickup and you can possibly walk there depending on what terminal you arrive.
They have a Starbuck's, a great bar with reasonable priced food, and the breakfast restaurant has a fantastic buffet.
Grapevine is on the northern edge of the DFW airport grounds. Small town but all the restaurants - Outback, etc., literally minutes from the airport, but taxi prices can be steep.
Best thing about Grapevine - the Outlet Mall!!! Off Sak's, Last Call (Neiman Marcus) and so on. Also good food court and movies.
If you want to stay at the mall, there's Embassy Suites that's connected to Bass Pro Shop (and Steakhouse). Also AmeriSuites, and more.
If you decide to stay at the airport, Hyatt will take you over to the mall for a fee - don't remember what it was...