Your best bet is to take the Yellow Line to Archives-Navy Memorial station and walk to the Mall from there. The exit dumps you onto Pennsylvania Avenue and you'll immediately recognize the US Capitol on your left as you emerge. The Mall is a block away and you'll be in the thick of the Smithsonian Museums and equidistant between the Washington Monument and the US Capitol. The Blue Line will only take you as far as Rosslyn on 7/4 which will entail a transfer to get to the Mall so you should stick to the Yellow Line. Be aware that the entire Mall will be fenced off and security will be very tight. Note that the Smithsonian Metro station (the only station on the Mall) will be closed all day.

NW arrives at DCA in Terminal A. The Metro station for DCA is between Terminal B and C. If you are up for it, you can actually walk from Terminal A to Terminal B in an enclosed walkway to get to the Metro station.