Two of my favorite cities! I love to do things slightly off the beaten path. So my suggestions may not fit all.
If you've never been to DC before, you'll of course want to see all the typical touristy things: Capitol building, the Lincoln and Jefferson Memorials, White House, Washington Monument, and all the Smithsonian museums... all of which are clustered around the giant lawn known as the National Mall. However, since I've been to DC countless times, I avoid all of that like the plague! LOL! I still love to see Arlington Cemetery... I saw Ted Kennedy's grave when I was there 2 months ago, very moving. The whole Kennedy grave area is one of the best places to view the entire city from too. Besides the touristy stuff, I LOVE shopping in the DuPont Circle and Georgetown neighborhoods of DC. Fabulous restaurants and bars in those areas... along with gorgeous old townhomes and mansions, scores of embassies and chanceries and such. When I was in DC a couple months ago I also tracked down the house and giant staircase from the Exorcist movie... that was fun! It's also in Georgetown... one of the prettiest urban neighborhoods in the country. The DC Zoo is really fantastic too. Oh, and use the Metro any chance you get... it's the most efficient and clean subway system in the US in my opinion. Saves you lots of headaches dealing with the insane DC street grid too. Oh, and if you like international culture and especially food... DC is the BEST! I think last time I was there I had Moroccan, Greek, Spanish, Italian, Thai, and several others... all authentic too!
No matter what you do in New York, you'll have fun. My favorite thing was simply just walking around Manhattan and hopping the subways to anywhere I wished. I especially enjoyed walking around the West Village and Greenwich Village... so pretty. Obviously Central Park is gorgeous too... and the buildings lining the park are spectacular (especially the Dakota building, where John Lennon lived and was killed). The Staten Island Ferry is a neat way to get out on the harbor and see the city... it goes past Ellis Island, the Statue of Liberty, and the best part is it's FREE! I didn't spend much time in Midtown when I was there... mainly a lot of office buildings and tourists. Lower Manhattan is neater... the Financial District is cool, all the buildings are so tight together, and there are old cobblestone streets. The Trade Center site is in that area as well obviously. I kinda hate I didn't get to venture into Brooklyn when I was there... seems there's so much going on there these days. Lots of art, music, food, and culture. I'll have to hit it next time around. I feel like I'm forgetting so much stuff! Have fun... I'm jealous!!
