We tried to hit 2-3 places per day - that way you can enjoy it without having to rush through.
Day 1 - Arlington Cemetery, Air & Space Museum, US Capitol and the National Mall
Day 2 - National Cathedral, White House (from the outside
), Lincoln Memorial and the National Mall (including all the memorials along the way)
Day 3 - Holocaust Museum, National Achieves and Union Station
Day 4 - we stayed at the campgrounds which turned out to be a good choice since it rained for the better part of the day.
I can see how you can easily spend a week or more there and still not get it all in.
We took the Old Town Tours in DC, it's a great way to see a lot of things and it's narrated so you get to understand what you are seeing. We did the same thing a few months ago when we were in San Diego.