I live around DC and your best bet is to not stay in the District. It's not worth the cost. You can find a better deal on a hotel in Crystal City, Bethesda, College Park, or any of the other areas right outside and they are all on the Metro Lines. You'll save a lot of money that way.
The heat tends to be awful here in the summer. I'm not a huge fan.
Do take in the Museums and the monuments. Though personally I don't like the National Zoo. I find it small and cramped and feel really awful for the elephants as they have such a small amount of space to roam in. However - there is an amazing Thai restaurant right off from the Zoo - so you might want to swing that.
Do see the National Cathedral - it's a wonderful structure.
If you want a tour of the Capitol Building - Call your Senator or Congressman's office prior to your trip and let them know you are going (hopefully they aren't Republicans

) They will make arrangements for a staffer to take you around and you can get in the gallery of either the House or the Senate and watch our government do nothing
The Supreme Court is also a great place to tour.
The White House is really not worth the effort to try and tour. Best bet is just to get the usual photo op in front of it. You'll save time.
Neighborhoods to check out:
*Dupont Circle
*Georgetown
*Capitol Hill
*U Street Corridor
*Adams Morgan
Be prepared for a number of things:
*security
*traffic!
*awful heat
Use the Metro as much as you can and not drive. It will be less mind numbing.
My G/F and I either Metro or Bike to work and its much more pleasant.
Hope this helps.