A tip: if you are only going to be in D.C for a few days, don't try to blitz every historical thing in the town. Between the Mall and the monuments, the museums, Capitol Hill and the White House, not to mention all of the good local stuff you seem so keen on, you need at least a week.
This is coming from a guy who tried to see the entire city in two and a half days. Damn budget!
^^^^^ I'll second this.
My first trip to DC many, many years ago was this pre packaged trip for kids at my school. Being rushed from one site to another just ruins the whole experience.
I do know that if you want to tour the White House be prepared to spend a half day waiting in line unless you have a relationship with someone that is capable of bringing you to the front of it. Depending on your time limitations it may not be worth it if you can't pull off a connection like that.
I don't know if the FBI is still doing tours, but I've heard that is pretty cool.
Williamsburg is pretty cool as well. Its a little out of the way, but the town is very pretty. The history there is interesting, but that isn't the sole reason. Just enjoying the food, beer, etc. in the old colonial town is a good way to spend an afternoon to evening.
Also, from experience taking a small plane ride over the Hamptons is pretty amazing.
And don't show up in Hell's Kitchen right at dinner time with no reservations you'll have trouble finding a decent restaurant anywhere that wont have you waiting a pretty damn long time.
That's about all I've got. I haven't been to either city that many times.