As someone that lived most of his life in the mid-Atlantic region, I can reiterate much of what has been stated already in regards to places to see. If you like museums, DC is by far the best option. The Smithsonian Institute around the Mall has a lot to see. The Holocaust Museum is worth seeing as well, but make that last, otherwise the whole day is a downer.
Punk D suggested staying in Philadelphia, which is a good option if you wish to see DC and NYC. If you want to stay in the DC area then Rockville, Maryland isn't too far out and is a nice suburban area where you won't get stabbed. As Durk stated, you can get into the wrong part of town quick in a lot of major US metro areas so watch out.
Orlando has Disney and Universal - otherwise it kind of sucks. But you aren't far from Daytona and you can take a 4 hour drive down to Miami, which is more or less a shithole IMO but South Beach and the Keys are nice.
Anyone telling you to visit the midwest is out of their mind. Don't listen. Ohio is one of the most boring places on the planet and Detroit is only nice for about 5 minutes in a 2 block area before getting seriously dodgy.
To be honest, if you are planning to fly from Orlando to your other destination, then you really aren't saving any time by not including the West Coast or other places into possibilities. Orlando to NYC isn't that much shorter than a flight out to Yellowstone, which is by far (IMO) the most spectacular place on the planet.
