The 100-400 is overkill. I'd bring it, but only for things like checking out the cracks on the Washington Monument or other such stuff, but it's totally unnecessary.
You need something like a 24-105 or anything similar to that. Try to just bring a camera and a lens. Leave everything else. Also make sure you have tons of memory and the ability to charge your battery, even while sitting around for lunch.
Flash photography is banned in most places. It's practically a religion to ban flash. I wouldn't even bother bringing it. I'd be much more likely to get a very small, collapse-able tripod that can fit in a small camera bag.
The places I enjoy shooting are:
Air and Space museum
Natural history museum
Outside the Capitol building
American history museum
National Archives (Declaration of Independence is on display, as is the Constitution---no flash...very dark inside).
The mall area (if it's springtime, summer or fall).
All the outdoor memorials on the mall.
Arlington Cemetery
Tons of other stuff.
Don't worry about the Whitehouse. That place is a crazy long wait, and they don't take you through most of it. The Capitol building is good, and you're allowed to shoot there (it's actually really cool), but they'll take your camera and put it in a locker while you go into the House or Senate chamber. They're really strict in there. You can't even draw or write unless you have special permission. They can't stop you from passing gas, however.
Don't worry about safety. During the daytime it's a much different than at night, and nobody is going to beat you up and steal your stuff. If you leave it unattended it will disappear, but the place is crowded in the daytime. You'll be alright.
Most important is to meet people and talk to them. Learn from them, especially the protesters (there are always protesters at the Capitol and Whitehouse).
One time I saw a group protesting against male circumcision on the steps of the Capitol. I am a jokester (and a bad one at that), so I said to them, "I agree. They need to cut that out."
They didn't think it was funny, but the people around me did.
There are no-nukes protesters at the Whitehouse. Tell them their display blows you away. Corny stuff like that.
More important than anything: meet some nice girls from other countries and states. Be polite to everyone you meet.
Have fun.


