The airport is midway between Fort Worth and Dallas and there is little of interest in the area that I remember. Your hotel will likely have shuttles to either city.
Oops...Tropic beat my post, and has much more recent experience in the *joys* of the D/FW area. (I never left anything behind that would cause me to go back there.) Billy Bob's is a kick, if you need a drastic antidote to the convention attendees, and the Stockyard's shops offer unusual purchase opportunities. You can buy those bull balls for that special someone, for example.
I am trying to imagine you wearing a Stetson and riding the mechanical bull.