Rick Lee nailed it, stay in VA. DC is a nightmare to drive and park, especially during the week.
I lived in the area and now come often for work. Sometimes my family comes along and we rent a car. We stay at the Key Bridge Marriott, it has parking for a charge, it's walking distance to the metro (Rosslyn) and Georgetown, and by car has easy access to highways route 66 and GW Pkwy. Some times they run specials on their site if you prepay.
For lodging in the DC/VA area you can also check
Washington.org - Official Tourism Site of Washington, DC