My 7 year old son and I just got back from a weekend trip to DC. We just took a backpack with a change of clothes. That is the way to go! We avoided the long line at the airport check-in as well as having to wait for baggage at each end and tips for people who handle your bags. A great time saver.
We did the National Air & Space Museum. They have Flight Simulators on one end which my son enjoyed. Also saw one of the IMAX films.
We got advance tickets on the computer for the Washington Monument. This saved a long wait in the line. Just picked up the tickets at Will Call. No line.
Did the Museum of Natural History. Saw a 3-D IMAX about undersea creatures which was really good.
Stayed at the Hilton Garden which we got on Expedia for $89 per night. Advertises at 3 blocks from the White House but those are LONG blocks! Had a metro station across the street, a CVS and a Subway nearby. However, I didn't know the metro would not be open on Labor Day. Had to take a taxi to the airport @ $15.00.
One tour I saw some people on that looked really cool was on Segways. I think it's a 2 hour tour for $65. They look really fun to ride on. Didn't see kids on them but the adults were having fun!
We had a great trip. Just remember everything is spread apart so there's a LOT of walking involved.

I have never heard of the Metro being closed for a holiday. Are you sure about that? Are you sure it wasn't just a matter of a specific entrance being closed due to lower demand and lower staffing?

The Metro calendar notes that on Labor Day there would be track work on two lines causing major delays. Implying that everything else was running:

http://www.wmata.com/calendar/default.cfm?nocache

Well, I was leaving out at 4 a.m. and the two guys at the front desk of the Hilton both agreed it was closed that day and even if open, it would not be running that early. They could be wrong. I could be wrong.

Metrorail is never open at 4:00 a.m.

Now you tell me!

Metro opens at 5 AM weekdays, 7 AM weekends and most holidays, including Labor Day. If you want 24-hour service, you have to go to NYC.