August is hot and humid, so be prepared to dress cool and comfortable! Frankly, even though I've lived here all my life, I do not love the heat and humidity here in the summer (I prefer the desert), but i know many people who don't mind it the way I do. And kids don't seem to care -- one of my best friends took his family to DC last summer (four young kids), and they had a great time. One of the upsides to visiting then is that you don't run into so many school groups (big crowds and buses) at the places you visit.
As for hotels, I have no real experience since I live so close to there, but I know people who like the Willard and the Hay-Adams.
You can literally spend days at the various buildings of the Smithsonian -- the Air and Space Museum, Natural History, Museum of the American Indian, etc., plus there are wonderful art museums as well, particularly the National Gallery, National Portrait Gallery, the Corcoran, Hirshhorn, etc.
I would highly recommend a walking tour of the monuments (my favorite time to do that is in the spring during cherry blossom time). The botanical garden on the Mall is one of my favorite places to go, and I also love the National Arboretum (further out away from downtown) -- there's a nice koi pond and bonsai garden, and miles of roads throughout that are great for a bike ride.
Six Flags is about a half hour drive from downtown DC. Or if you drive an hour south you can go to Kings Dominion, but that means dealing with Northern VA traffic.
If you decide you'd like to get out of DC for a day, historic Annapolis is a nice side trip (45 min drive), or you can swing up to Baltimore for the cool respite of the National Aquarium and the Visionary Art Museum (45 min drive). Fort McHenry is interesting to visit as well. Lots to do around here!