A few years ago, my husband and I took our first child with us to Washington D.C.. My daughter was too young at the time to know where we were, but it was AMAZING for me! I had never been there but of course I've always seen replications of the places there on TV or in film.
There are so many things for them to see. Most of which they've only seen on TV...the White House, Washington Memorial, Lincoln Memorial, Capitol Building, Arlington Cemetary, and of course all the many FREE museums!!
I recommend watching some films that feature Washington DC before you go because it makes your experience more fascinating. For instance, if you watch National Treasure -- it will help you create an itinerary of places you may want to see...and there are sooo many. Just think about it...there have been hundreds of historical events that took place at our nation's capitol. It's like walking around one huge landmark. You can teach your children so many history lessons here! Show them old pictures of historical events like MLK's famous speech in front of the Washington Memorial.
I also recommend not going during the summer because it's extremely hot and humid. If you can-- try finding someone that could get you into the White House for a tour. It's a lot harder to do now (a lot of security/background checks) but it's totally worth it!