I assume you mean DC, not State. Based on that,
1. The Smithsonian Museums. Even if you don't care a whit about art, the National Air and Space museum and the Natural History Museums are awesome. The art galleries, National, Freer, and I can't remember all the others, are fantastic too, just wanted to point out that there's more than just paintings in the complex. Of course, you can check out all the monuments and memorials on and around the Mall - and ALL of these are free. Budget or no, free is a good price. You can even just drop in for a half hour or so, look at two things and go, no guilt.
2. The Millenium Stage at the Kennedy Center. Also free, they have a performance at 6 pm every night of the year. You can check on-line to see what's up, or just do what we did whenever we were in town in the evening. Stop by and check it out. If it's not to your taste, you can always leave. We were often surprised, and almost always intrigued and or delighted enough to stay.
3. Plane-spotting. There's a big park near Reagan Int'l where you can watch the comings and goings, and relax in a waterfront park. People are walking their dogs, playing frisbee, whatever. It's relaxing.
4. Mount Vernon. Even if you don't go inside, it's nice to walk around the grounds.
5. Get a metro card and go EVERYWHERE by metro and bus. There is no need for a car in DC, we lived there a year with four kids and didn't own one. Cheap and easy. I believe they have a "sightseeing by metro" map that tells you places you can get to by transit, pick one up and see what interests you. They don't just focus on sights, there are neighbourhoods with interesting appeal too. For example, Alexandria is popular just for walking and watching.
6. Georgetown.
7. Get off the metro at Dupont Circle, don't get killed crossing it (an accomplishment in itself) and just wander in the neighbourhood.
8. The Canadian Embassy usually has a bizarre programme of events going on, you can always stop by and check that out. There was a short animated film festival going on one time we went there. Pretty funny stuff.
9. National Shrine. This is the largest Catholic Church in North America (I'm almost certain) and I believe the 8th largest in the world. And is unlike just about anything else you'll see anywhere in the US. It's mostly Byzantine in style, lots of mosaics and quite astonishing. Along the side walls and downstairs are dozens of small chapels related to Marian apparitions - Lourdes, Fatima, Guadeloupe, Siluva, Czestohowa (sorry, spelled that all wrong)... if that's of any interest. Even if you're not a churchy person, a visit to the Shrine is interesting for it's architecture and art. It's interesting to realize that even though it's been in progress for umpteen years, it's not finished yet. The plans are for even MORE mosaics. The Washington National Cathedral is completely different, neo-Gothic and ornate and has great organ recitals if that floats your boat.
Sorry, my sister-in-law recently moved to the DC area and I've sent her all our guide books, so I'm just going from memory and experience here. Eyewitness make a good Washington, DC guide book you might want to either talk your dad into buying or check it out from the library to get a preview before you go. Plump for dad buying it, it's worthwhile, and nice to have the maps/metro info right handy.
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