The W.H. and Congress are separated by about 1 1/4 mi if you go by the diagnonal street Pennsylavania Avnue. 1/4 mile longer if you go by 15th Street and Constitution Ave, due E and N, or S and W. The best metro stops are near the museums and Congress by a few blocks. The museums are mostly on Consitution and Independence, offshoots from Congress running E/W.
WH physical tours appear limited to US nationals with 1 month advance reservations - a post 9/11 restriction. Congress allows tours, but not browsing. Virtual tours. If you have a Yankee friend, esp. one who lives in DC, they may be able to get you better tickets through their Congress-person.
Museums no restrictions. Some Gov buildings of interst on Pennsylvania. Parking is problematic, but if you plan to park all day and come in with rush hour, one option is parking is Rosslyn, Va, near Metro stops. At that distance from DC, your "rush hour fare" will be trivial, although you still have to wait until 9:30 to use the "all day passes." Another option, if you pay the higher parking prices is DC bus passes for $3 each, and truly is all day.