As GoingAway mentioned in an earlier response, your best bet is probably renting a car and storing your bags in the trunk. You can then drive into the city, save on transportation into the city (cab fare is about $60 O/W; bus + Metro - departing every 30 minutes - about $12 O/W, Metrobus - which goes every 40 minutes during peak periods, hourly otherwise - is $3.10 O/W), and go directly where you want. As "airport traffic," you'd be able to use the HOV lanes on I-66 both to and from the airport. Parking in the city can be costly but, depending upon the day, arrival and departure time, and location, you should be able find something for less than $20 for the day.