I love Boston, I grew up in NH and I would go to Boston (take the T in from Bradford) on a monthly basis.
Another vote for the aquarium! Then, hit Quincey Market (right there) and have dinner at the Legal Seafoods that is right there.
Also, the Museum of Sience is fun (The 'Museum' stop on the Green line, just north of North Station) for kids and adults, the Computer Museum is also fun (near South Station)
The Boston Commons must be beautiful this time of year, too.
If you're feeling adventurous, head up to Dover Point, NH and have dinner at Newick's (just off of Route4, west of the bridge).
If it's cold, head over to the Cambridge-side Galleria (if it's still called that) or into the theatre district (Boylston St?) and see a show. If the Boston Pops are in town, and playing, that's definite if you like classical music.
Head south to Newport, Rhode Island (and Mystic CT) or for a real adventure, head up 95 to Freeport, Maine.