We went to Washington DC last June and had a great time! It was our family's first visit. We drove and stayed at Hotel Lombardy on Pennsylvania Ave. It's a very charming boutique hotel that has tons of character. It has a manually operated elevator with attendant! My kids thought it was so cool to "drive" the elevator. I found a
AAA rate through Travelocity which was cheaper than the hotel website's AAA rate. Our rate averaged $140/night, which isn't bad for in the city. Weekend rates are much cheaper than weekday rates. Parking was an additional $35 or so per 24 hours. The hotel is about 4 blocks from the White House and 2 blocks from a metro station.
Since you are driving, I highly recommend a day at Mt. Vernon if you haven't been. We spent an entire day there and the whole family LOVED it! Purchase tickets online in advance to bypass the line at the estate.
You can also get tickets for the Washington Monument online. We had to pay $1.50 each to have them mailed to us, but that was sooooo worth not having to stand in line for tickets! We had the first trip up the monument for the day.
Another cheap but great activity is DC by Foot. It's a tour company that gives free walking tours of the monuments. The guides work for tips only. We found the guide to be very well informed (he had a degree in American History) and very entertaining. We started near the Washington Monument and concluded at the Lincoln Memorial.
The Smithsonian museums are fantastic! Our favorite was the Museum of Natural History. I'd read lots of advice about not eating in the museum cafeterias, and I would whole-heartedly support that if there was another alternative closeby! We had a marathon museum day where we went to three of the Smithsonian museums. We were starving and ate in one of the cafeterias. It was the worst meal we ate and it was over $50 for fast food for four. You're kind of a captive audience, though.
This is getting long, so I'll end here. If you have any other questions, feel free to PM me. Happy planning!