Recommendations for rest stop (gym/spa)

Here's what it comes down to:
I seeking a place that I can work out, rest my eyes and then have a shower before a work conference. Does anyone know of a luxury gym or health club that I could get a day pass to and accomplish this? My flight options are kind of limited and I'll arrive at 9AM with no rest (change-overs at weird times). I get angry without rest and I'm someone who dresses cozy for a flight. I need somewhere as a base to rest (I'd settle for a nice pool chair) and shower. Thanks in advance!