I think Downtown or Dupont Circle would be good.

I stayed at One Washington Circle. It's very close to the metro and each room has a little kitchen. I was very pleased and would stay there again

http://www.thecirclehotel.com/

remeber if you are going to the capital you need to schedule in advance. check online.

For under $500 a night, you should have your pick of places and I would agree that downtown or Dupont Circle would be good areas to choose from. Given you've got two children between you and your friend, pick from one of the suites hotels (Homewood, Residence Inn, Doubletree, Embassy, Carlylse Suites) or look at the slightly more upscale Kimptons (Palomor, Monaco, Madera, Rouge, Helix, George) which often have oversized rooms.

When are you visiting?

Thank you everyone. The Kimptons seem to get phenomenal reviews on tripadvisor. I think we may go that route.

Then look at the Monaco (downtown), by far the best located of the DC Kimpton hotels. The Palomar is also a good location (Dupont) and has larger standard rooms.

I love Kimptons. Each hotel has its own history.

The Madera, the Rouge and the Palomar were all originally apartment buildings which explains why their rooms are generously larger (increasing in size from the order listed) than your average downtown hotel room. Palomar & Madera are a five minute walk to the Dupont Circle Station. The Rouge is a 10 min walk.

The Monaco is a gorgeous hotel, a 19th C. landmark building originally home to DC's Post Office. The rooms vary more in size. I would steer you away from the rooms on the "first" floor which are slightly below street level.