You don't HAVE to leave the airport itself.
I've had on more then one occasion a layover date where the man has rented a room at the Hyatt  for a few hours (I think it is in terminal C)     and I've arrived to the room for our time together.

Not sure what the men said to rent the room for a couple of hours but probably not uncommon.. maybe a travel would be on their way overseas and wants to take a shower and rest for an hour on a bed before a long flight?  
Sure the hotel could not give a fig why but I know sometimes men feel guilty and it makes them think everyone knows (and cares) they are being naughty. ha ha

In that case you needn't find a woman in close proximity to the airport .. only a lady with a good reputation that she arrives in a timely fashion and isn't prone to 'no shows'.

hope that helps.  
ALEA

Related Link: Here is a link to the GRAND HYATT dfw. If you want to explore this possiblity further. cheers!