First off, no Taliban clothes, unless you have a fetish for cavity searches and receiving incredulous stares.
The East coast is the place you want to go, the West coast doesnt have anything comparable to NY -- The greatest metropolis created by MAN period (No
exaggeration, I've been to quite a few great cities around the world, NY is the best!)
If you are on a budget you might want to take the sketchy China town bus to DC and Philly or you could go by train or bus or plane. Train is
preferable as you get the feel of travelling and less security check hell.
As for staying in NY, you should try to live somewhere in Midtown Manhattan or the village. These are some of the best and most convenient places to
stay as these are pretty lively places. Also try to look around during the week as during the weekends and Friday , as you have out of towners who
just cram up all the clubs, pubs and other joints. The village has so many excellent little places that are worth exploring. Then you could check out
Harlem and the jazz scene there. (Dont worry about getting mugged etc, NY is a pretty safe city now. You wont find trouble unless you look for it! )
There are many ways of checking out lady liberty, my best way is the Staten Island ferry even though you just pass by. You can also take a helicopter
tour of Manhattan and the surrounding if you are really keen. If you have never been to Times Square, a quick look is advisable since it is supposed
to give you that "center of the world" feeling.( to outsiders anyway! )
DC is only buildings and museums so if you are interested in that kind of stuff a day or so should suffice. But if you are looking for 'life' NY
wont disappoint. Philly also has a lot of culture and life with its own unique flavor.