this is exactly what I was going to say...hit DC's fabulous museums. the nat'l museum of art & smithsonians (air & space, native american, natural history)...then go to the monuments: lincoln, jefferson, washington...visit the capitol if you can. of course barhopping in georgetown like the OP suggested is super fun...also visiting old town alexandria.
Plus don't forget the Public Library in New York,, I heard its more than a hundred years old !!!
I'd go to New York (Central Park, museums, broadway shows) , Boston ( tour around the universities' campus) , San Fransico (just being their is enough) , LA ( if you're a big fan of celebrities and Hollywood)..
I'll try their Sprinkles cupcakes + JohnnyCupcakes and the yogurt with fresh fruits place...