Can you go sightseeing in DC using the metro and walking?

Yes, in fact that is best way to travel to save money from parking, avoid traffic, and get everywhere much faster. All major sightseeing points pretty much have a metro stop. Your best bet is to park at a metro stop and just ride the metro all day to do all of your sightseeing. For even more good answers regarding this you should also check out askalo, a site dedicated to city Q&A.