As Redskins season ticket holders living in Virginia Beach, we know the DC area hotels very, very well

. Definitely stay outside of the area near a metro station rather than in DC proper - cheaper (or free) parking, cheaper rates, quieter, etc etc. Some of our favorites:
Fairfax - Courtyard Marriott Dunn Loring - directly across the street from the Dunn Loring Metro station (orange line). Free parking. Quiet. Near Tyson's Corner shopping malls. A lot of weekends they have a 94/night rate which includes breakfast for two adults and kids under 12.
Arlington -
Residence Inn Pentagon City - about a 10-15 minute walk to the Pentagon City Mall, which has a Metro stop in the mall (blue and yellow lines). Very nice, free breakfast, reasonable weekend rates. Parking is about 18 or so a night.
Hampton Inn Crystal City/Reagan National Airport - about a 5/10 minute walk to Crystal City shops, which also has a metro stop (blue line only, I believe, but might be blue and yellow). Free breakfast, reasonable rates. Parking about 12 a night if I remember correctly.