Take a taxi or shuttle bus to the Herndon Marriott at Worldgate -- right next door is a huge sports club at Worldgate -- you can get a day pass, and there's a large pool, all kinds of workout equipment, running track, basketball, racquetball, etc. Also a sauna and jacuzzi. Spa services, but you probably have to reserve in advance for that. I'm sure they won't mind if you take a nap on the lounge chair by the pool!
I used it once, when I had a redeye into Dulles, and I wanted a workout before business in Reston. Indeed, I returned at the end of the day for another workout and to relax before heading in to D.C. I would definitely use it again if I had a full day out there.
Worldgate Sport & Health Club
13037 Worldgate Dr
Herndon, VA 20170
(703) 709-9100
www.sportandhealth.com