DC quiet? Gosh, there's tons of stuff to do there.
No school I went to ever had anything like that, but I actually know someone whose daughter went on a school trip to DC (from the Midwest) the summer between seventh and eighth grade. She did have a great time. If one of my kids had an opportunity like that my main concern (other than the obvious--what's the itinerary, will the chaperoning be good, etc.) would probably be, are whichever friends of theirs are going the sort of kids who'll be genuinely excited about the historical and cultural and political stuff, so that the character of the experience doesn't wind up being more like one giant blowout slumber party. Not that there's anything inherently wrong with that I guess, but for that kind of money...