I live in the northern suburbs about 5 minutes outside of DC (red line metro stops). We often get hotel rooms for people who are visiting our church (like visiting minister's etc.) using Priceline. The one we usually get a good price on is the Hilton in Rockville, MD. It's about 2 minutes away from a metro stop.
I would visit during the week. I don't think summer is the best time to go because of all the tourists, but if you plan extra time for seeing things it probably wouldn't be an issue.
The National Zoo is great. It is free and you can take your own snacks/water/etc. You can take the metro and a short walk to get there.
The Air and Space Museums are great too. They have a schedule of events online that you can look at. Many Saturdays they have special events going on.
There are TONS of museums, memorials and the botanical gardens located in between the Capitol building and the Lincoln Memorial. Wear really good walking shoes and plan more than one day to do it all. I've heard the Treasury is a great place to go

. Apparently you can watch them make the money. We haven''t made the time to go there yet.
If you want to stay
IN D.C. I recommend finding something in NW D.C. It is by far the safest area (even though it has bad spots too.), please stay away from SE it's just not safe. (No offense to anyone who may live there).
If you plan on flying into Reagan National Airport they have access to the metro system, so you don't even need to get a cab or anything.
If you stay on the north side of D.C. then New York is only about 3 1/2 hours away. They have bus trips that you can take. You can leave early in the morning and get back about 11pm. My husband and a friend from Russia did it last year and while they didn't have time to see everything our friend wanted to, it gave him a taste of it.
Also, Baltimore is accessible by Amtrak.
There's so much to do around here it's hard to pick the best. If you have any other questions please let me know. I'd be happy to help!