What about buying a franchise of a gym like Planet Fitness or something like that? That way you would tap on an existing member base as well.
I would most likely only pay with enough of a layover. I try to avoid long layovers. If you stuck one in CLT I would just make it my main gym and buy a membership to it.
Per visit I'd pay $10-15. Maybe up to $20 if the shower came with a toiletry kit like the airport showers.
Per month I'd pay $20-30. Maybe up to $50 if it includes other airports I use as well.