Several years ago, I had a number of very good experiences at the Loew's hotel, which is a few blocks South of the mall. Loew's has a metro stop under it which directly connects to DCA (but you're probably flying out of IAD). However, the convenience of the metro makes it easy to get back to the hotel, so that you could check your luggage the morning you are leaving, have some time to walk around, and then use the metro to get back to your hotel to collect your luggage and get to the airport. In any case, I suggest staying at a hotel close to a metro so that you can use it to cut some travel time in the city, although taxis are fairly reasonable.

Some of the hotel chains (Marriott comes to mind) list better weekend rates on their websites than on the general travel sites. DC is a suitcase city and, unless there is an event that weekend like the Cherry Blossom, weekend deals will likely be plentiful.