Speaking as one of the other Bostonians on the board...
The Museum of Science is pretty darn neat for all ages. Kind of light in some areas (as it's designed for the general public - otherwise they wouldn't make money!), but a lot of fun once you get into it. Plus the Omni Theater and Planetarium shows tend to rock, assuming you stay away from the kiddie programs. (Though I've heard good things about some of the kiddie programs at that.)
The MIT Museum is kind of small, but also nifty. They have the Hall of Hacks (a room containing a number of relics from the various practical jokes students have played over the years - including the fake police car that was found on top of the cupola one year, and the fiberglass cow that had appeared there a few years prior) and what I've heard is the world's largest collection of holograms. (Or at least they did the last time I was there.)
Plimoth Plantation is a bit out of the way, but worth visiting if you have the time. It's a living history museum recreating the original settlement and a Wampanoag (I hope I'm spelling that right) - local Native American - village. (The folks at the Wampanoag village dress authentically, but are never "in character," for various reasons.) You can also visit the Mayflower II on the shore of Plymouth proper, and see the Plymouth Rock.
The various trolley tours of Boston can also be quite enjoyable.
The Museum of Our National Heritage (I think that's what it's called) in Lexington (*sigh* - I *think*) is pretty neat. I haven't been there in a while, so I don't know what's there now, but I do remember that they always had interesting exhibits.
The New England Aquarium tends to be interesting as well, as are the whale watches that depart from that general area. If shopping's your thing, you've got to visit Faneuil Hall - heck, it's fun just to LOOK. I love their joke/novelty shops. For Cheers fans, there's the Cheers restaurant at Faneuil, and the Bull & Finch Pub some ways away. And I think that covers all the places I tend to favor.
Lessee...as for things you should avoid like the plague...well, I can't think of anything offhand. I would caution against the Tea Party Museum, which is pretty dorky; but if you don't mind silliness it can be fun.
Phew. Well, I've probably given you a case of information overload...but you DID ask.

Just try not to laugh at our outrageous accents. (Oddly, I don't have one, but a lot of the people around here do.)