From the Sheraton Reston, as others have stated, you could drive to either the West Falls Church and take the Metro or try this --

Just a few miles away from your hotel, back towards Dulles, is the Herndon-Monroe Park & Ride. Amazingly, parking is free. From there, you can catch the Route 5A Metro Bus, which is an express bus that runs on the weekends. The buses stop at the Tysons-Westpark Park & Ride, which is about the same distance east of your hotel as the Herndon-Monroe Park & Ride is west and then head right into DC. The 5A bus is an express bus that stops in Rosslyn and the Metro station and at L'Enfant Plaza very near the Air & Space Museum.

The 5A bus costs $3.00 each way. The last bus leave L'Enfant about 10:30 in the evening, so you'd have more than enough time for an early dinner somewhere.

Here's the link to the bus schedule: Metro Bus 5A