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Being a beer fan I also love the Commonwealth Brewery.
New England Aquarium.
Little Italy (or the Italian quarter in the North End) is a good place to eat but it can be a wee bit pricy.
If you want to eat really cheap go to Faneuil Hall Market Place (AKA Quincy Market).
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.
By far, Newicks is the BEST seafood place I've ever eaten at. The Weathervane (has to be the one in Kittery, the rest aren't good) is good and Legal Seafoods in Boston (near the aquarium) is good.
I remember running to Sander's lobster pound in Portsmouth to get FRESH lobsters, 1.5-2 pounders (you really don't want anything bigger than that!).
Sometimes I miss northern New England. Sebago lake, the Kangamangus, Route 101 (both ends), The Old Man (how sad), etc..
Oh, to the OP, if it's baseball season, you HAVE to go see a Red Sox game, Boston has the most loyal fans out there and just walking around Fenway is an experience in itself (not a bad one). Just don't say the Y word (that so-called team that is in New York). ;)
You need some spelling corrections:
Lobster stew and a pound of steamers there once a month.
It's "Lobstah Chowdah" and "steamahs". ;)