If you fly into Boston, you could take Amtrak from Boston to NYC, then from NYC to Philly, then from Philly to DC. Most of the train stations are either downtown or a taxi-ride away from downtown. You can then pick up the rental in DC and avoid all the car issues of those major metro areas. On the other hand, if you've ever driven in London, than NYC should be manageable, even easier since most of Manhattan (the borough where all the tourist stuff is) is a grid. The only thing that gets expensive is the parking. The scenery from Boston to DC along the main highway (I-95) is underwhelming and very unrepresentative of the area.
Amtrak has a (relatively) high speed train connecting Boston to DC and the cities in-between. It's called Acela. Check out
Amtrak.
When I take people around New York, my first stop is the Empire State Building. The view from the top is stunning and you get to see the lay of the land, as it were. From there, Times Square, Rockefeller Center, Central Park, United Nations, and others are all within 30 minutes walk North, and quieter places like Greenwich Village, Soho, Chelsea, and Meatpacking are within 30 minutes walk South and West.
Enjoy!