North Conway, New Hampshire: New Hampshire is one of the most beautiful and rustic states in the country, and North Conway epitomizes so much of what New Hampshire represents - and if you are traveling around New England, one of the best things about North Conway is the fact that it is very much a "tourist town," which makes it easy for you to get the taste of everything you want to get the taste of.
Ogunquit, Maine: If you have never been to New England before, your idea of a "beach town" might be a bit different from a New Englander's idea of a "beach town," and when you go to Ogunquit, Maine, you will be able to see and experience a New England beach town in its fullest sense.
Plymouth, Massachusetts: Plymouth is one of the best places to go to go if you are wanting to get your fill of "historical and beautiful places" - as you will be able to see Plymouth Rock, the Mayflower II, and a beautiful small town that grew from the first permanent (and lasting!) settlement in America.
It is pretty difficult to choose a "wrong" place when you are traveling around New England, but with these spots in mind, you will be sure to catch some great sights and to capture some truly wonderful memories.