I was out there in 2006 and we stayed at the Fairview Park Marriott in Falls Church (Cat 4). It's a little ways out of town (and on a beautiful plot of wooded/secluded land so you don't feel like you're right off the highway), but they have a free shuttle to the metro station, so we just took that to the metro, then used the metro to get around town. Maybe 20 minutes or so to get into the heart of DC, but well worth it, I think. The next time we go, we'll definitely stay at the same place.

The only thing I would do differently is not pay for the taxi from the airport - take the metro (DC's system is clean and easy to use) to the Dunn Loring metro station, then have the hotels metro shuttle pick you up -- no need for rental cars or taxis the entire trip.