I live just outside Boston.
Definitely have lunch or dinner in the North End. Lots of great Italian restaurants, and the home of Paul Revere, which you can tour.
Close by is Fanuel Hall... Durgin Park is there... oldest restaurant in the country. and also the Union Oyster House just a couple of blocks away.
Museum of Fine Arts. There is a recent addition that is spectacular! Close by is the Isabella Stuart Gardner Museum...and if you time it right, there is music from some members of the Boston Symphony... you can hear the music throughout the museum. I'd suggest visiting Symphony Hall, but most of the musicians are away.at Tanglewood in western Mass for the summer season.
The Kennedy center is just south of Boston.
If you like to shop... Newbury Street... great shops and restaurants... and while you are there, the Boston Public Library is worth a visit, and it's just a couple of blocks away.
MIT Museum...in Cambridge right on Mass Ave. if you go, eat lunch across the street at Sydney's at the MIT hotel.
Boston Science Museum...
You can ride the the Swan boats and visit the Boston Common... then take a walk up to Beacon Hill...you can even walk by John Kerry's house in Louisburg Square on Beacon Hill.
If you want to venture a little further... Quincy is just south of Boston, and you can tour the home and birthplace of John Adams and John Quincy Adams.
Plymouth is about an hour's drive south and is the home of Plymouth Plantation and the Mayflower. Plymouth itself is a Quaint little village with a lot of preserved history. There's also the Fairbanks House in Dedham, just south west of Boston. Built in 1634, and still standing.
Along your drive to Maine, you might want to take a detour and stop in Salem... home of the witch trials... or Marblehead, which is a gorgeous town on the water north of Boston.
There's lots more but that's a start.