I would recommend doing a google search for a place to rent from in floridia, i know just about every major airport up north here rents out basic four seater training aircraft. You might however, have to make some sort of pre arrangement with the airport to rent for an extended period of time.
As for points of intrest in the eastern/mid USA? if you're going to be flying from flordia, be sure to go to Key West, or Daytona Beach, and if you're into theme parks, visit Disney World. (is it world in flordia)?
Going further up north, there's this cool place right on the border between South Carolina and North Carolina called South Of The Border, its a neat little place to stay overnight. Of course, if you're going further up north, Washington Dc would be a nice place to visit, and still further up north you could come visit my hometown of Pittsburgh Pennsylvania
Thats all i can think of at the moment, ive never really been away from the east coast so i wouldn't know about out west.
Safe flying 2 all
T13x