In recent years, we've used the Holiday inn Express, Grapevine, just outside the North Entrance to DFW (currently cluttered with road construction). Well managed, a decent breakfast, courteous staff, shuttle runs "on call" (and I've been hauled both too and from the car rental terminal). We commonly stay a night either before or after trips in exchange for leaving our car while abroad (No help to you!), and find this modest caravansarai comfortable and accommodating.

The Grand Hyatt seems a bit expensive, but may be the most convenient for you, with easy access to the shuttle bus to the rental terminal. My decision would be based on arrival time and immediate plans thereafter.

Welcome to Texas, a very big place in which distances may seem far, but driving times more manageable than expected.