First of all, there is no Metro in Tysons Corner or "Fairfax". There is a West Falls Church Metro, an East Falls Church Metro and a Vienna Metro.
Having said that, it would probably be better for you to choose a hotel closer to D.C. than Falls Church or Vienna. Why not look at hotels in Arlington near the Metro stations of Crystal City, Rosslyn, Courthouse, Clarendon or Ballston? If you are looking for free parking, I can think of 2 hotels off the top of my head that offer free parking and are within walking distance of Arlington Metro stations: Best Western Iwo Jima (Rosslyn) and Americana Hotel (Crystal City). I'm sure there are even more choices that have free or relatively cheap parking.
Thanks for your suggestions. The other issue is that our friend's wife will be driving up from Charlottsville to meet us also, and I am trying to find a place that works for all of us, and gets her there in time for dinner.
The Marriott Courtyard Dunn Loring may meet your needs -- it is a block from the Dunn Loring Metro.
If you go around the Beltway north to Rockville Pike and drive north to 1750, you'll find the Hilton on your right which is on the Metro heading into Downtown D.C. The station is just across the parking lot in the rear.
Wow, the Marriott Dunn Loring sounds perfect!! We've never heard of Dunn Loring, and neither has our friend in DC.
Thanks very much!