Hi there! I work in the travel industry in New England so hopefully I can help. The idea of a "New England" tour is a very popular package. One that is most popular in the fall.
Many people who do the package do start the tour with Mystic and enjoy the Mystic Seaport as well as the Mystic Aquarium. From there, they drive to Newport, RI. Spend 1 night in Newport and do Newport in the morning. (Most affordable way to stay is to stay either in Middletown or in North Kingstown, RI not Newport as it is expensive in the summer. Newport is beautiful. The Cliff Walk is great for the teens as long as they are physically up to it (it is a lot of walking)... and tour the mansions they are beautiful (one or two is fine ... they all start to look the same after a while... usually people choose Breakers because it is the largest and Rosecliff because it is where the Great Gatsby was filmed).
From Newport, they drive to Cape Cod. I recommend staying in Hyannis because it is a central point from everything and most of your chain hotels are located there. (Holiday Inn, coming soon Doubletree, Marriott) I would allow a few days in Hyannis (3 or 4 depending on what you can do). Visit Provincetown (very eclectic, gay, artsy community, family friendly during the day and more fun at night), also visit the National Sea Shore to see some beautiful untouched beaches (on way to or from Provincetown). Spend one day at one of the islands (Martha's Vineyard or Nantucket (ferry required)) I reccommend Nantucket because it is smaller, more quaint and easier to navigate and discover in one day. Also great for renting bikes and biking the whole island in one day. Sandwich is another great place on the Cape, with a glass blowing museum, antique car display and others.
On the way from Cape Cod to Boston stop in Plymouth. Spend one full day in Plymouth doing Plymouth Plantation and the Mayflower. Good history lesson for the family. Do not stay the night in Plymouth though, continue into Boston.
If you are trying to save money, at this point, I would get a hotel room in Braintree or Quincy or somewhere on the "RED LINE". The red line is one of the 5 colored Subway lines that go in and around Boston. It is much less expensive to stay outside the city and the subway is only about 15min to 30 min depending on traffic. During the day, visit Boston Museum of Science, Prudential Tower and Museum of Fine Arts (I really recommend you purchase something called the Go Boston card which includes admission for Newport, many Cape Cod attractions and many Boston attractions as well as more to come in order to make it more affordable (I did it for Miami and it was great!)) At night, go to Fenway and catch a game. Even if you aren't a Red Sox fan, the environment itself creates a memory.
From Boston, travel along the coast to Salem, MA. This is where the famous witch trails were. This is some place that you can just stay for the day and continue more north, or you can do an overnight.
From here, you can either head home or continue further north. Depending on what direction you go to the north the sites can become far and few between with long driving between sites. Where as the other previously mentioned each is within an hour drive of the next.
If you choose to do New Hampshire, I'd recommend either the beaches or the mountains, not both. Or you can shoot of and head to Vermont, where as others have said, you can go to the Ben and Jerrys Factory, the Cabot Cheese Factory and more all in one day. (I've set up a whole day long tour based in a small area just as a Vermont food tour ... yumm
)
That just about does it. I've lived in RI and Cape Cod, spent a ton of time in Boston and I know Vermont and New Hampshire so if you need or want more info., hotel info etc. Or if you want some Cape Cod brochures mailed to you, send me a private message. If you don't mind waiting a little bit I can even get you some RI and Boston brochures too!
Happy Travels!