NY:
NYC: Museums Natural Museum of History, the Met, MOMA (if you like modern art), Broadway, 5th Avenue, Central Park, The Bronx Zoo, China Town, Little Italy, Hoboken (take the PATH train) for the view of NYC, a nice dinner, and a cake from Carlos Bakery (e.g. Cake Boss), Times Square, Radio City Music Hall/Rockefeller Center, Empire State Building. If you like nightclubs go to Webster Hall.
PA: Take a trip to Philadelphia (two hours from NYC by train or car): Liberty Bell, the art museum, Chestnut and Walnut Streets. If you like nightclubs go to Van Gogh or Egypt.
From PA take a train to DC (Another two hours): White House, the Smithsonian museums (so many), site of Lincolns assassination, the National Mall (which isnt a shopping mall by the way), so much more to see. If you like nightclubs go to Lotus.
Should you want to or have time to continue south Shenandoah National Park is a couple of hours away by car but IMHO not nearly as striking as the national parks on the West Coast
LA:
Hollywood
Disneyland
Venice Beach
Beverly Hills
San Diego
From LA you will be three hours from Las Vegas should you want to drive there. Its a drive through the desert, but it somewhat interesting. If you do go to Vegas you will be a couple of hours from the Grand Canyon, Zion National Park, and Bryce National Park which are all absolutely breathtaking
San Fran:
You will be very close to Yosemite National Park, Sequoia National Park and Lake Tahoe.
Enjoy!