I've visited DC semi regular over the last 15+ years.
1. stay out side the beltway, and get a metro map.
2. stay near a metro station, preferably a park and ride one..(weekend parking is free. I think evenings are as well.) Park and ride is cheaper than cab fair, a bit more than bus. (I think you can get transfer slips from bus to metro, have never done that one myself. Those would reduce the fairs.)
3. nearly everyone in DC can tell you what station they are near. You should never have to make more than one train change. The trains all cross paths in at least one location. Most of DC is within a few blocks of one of more stations.
4. If you think driving into DC will save money I can assure you it will not most of the time. Don't park on the street in DC. (If you don't get broken in, the bizar parking rules will likely get you a fat ticket or towed.)Parking can cost as much as 20-30$ depending on where you have to go.
5. Do make sure you exit the "right end" of a station. Exiting the "wrong" side can add a block or three to your walk. Stations are nearly all fully manned. Ask if you aren't sure. (The sign work takes a hair of getting used to.)
I never drive into DC anymore for anything, even with groups of people. The metro goes nearly every place. It's clean, fast, not very expencive and easy to get around. If the metro doesn't go directly cabs and busses will get you the last bit.
The DC metro and NY subway systems are the best. (You can't pay me to ride Septa in PA. What a pile of crap that system is.)