If I were going out of the airport a while - as I have when I've visited the C R Smith Museum, for example, I leave my bag in one of the lockers in one of the DFW Admirals Clubs (I think A still has these, as opposed to luggage shelves.)

Leaving it overnight might well be a no-no, but for a few hours, if you have access, it should be OK. If the club is pretty empty and they notice you, a cheery "I'll be back" should do it; seems to work for California's governor.