Actually, Fenway doesn't have to be expensive. Go for the bleacher seats. Sure, they're way out there, but Fenway's a small park. And for kids they're more fun, because that's where all the rowdy beachball tossin'/wave starting fun happens. Just beware the cursing, and bring sunscreen.
I heartily reccomend the Museum of Fine Arts, a world class collection, and they've done a lot to make it kid friendly. Take in a whale watch, they're good fun. For a cheap tour of the harbour, take one of the commuter boats, they take the same route as some of the expensive tours, for a few bucks.
A walk up Newbury Street is a fun shopping experience, and a stroll through Beacon Hill (hill and flat) and down Commonwealth Mall is a great tour if you enjoy architecture. Don't miss the USS Constitution, 'cuz battleships are cool.
One of my favorite spots in town is the Copps Hill cemetary, in the North End. It's the oldest burial ground in the city, and is full of little stories. Find a good guide book or pamphlet, because many of the headstones have little stories behind them (like the stones pocked with bullets from a Revolutionary War scuffle). I set a Call of Cthulhu game here once.
If you can get a car for a day, a trip out to Lexington/Concord to the North Bridge and Minuteman Park is very interesting, and a beautiful walk. Sturbridge Village or Plymouth Plantation are both good historical villages, with people in period costume, doing work and giving lectures on the time. One's an hour west and the other's an hour south of the city; no need to do both.
Do NOT, repeat, DO NOT, rent a car, if you will be staying in the city. The subway (the T) is an excellent system, and visitor passes are cheap. Parking in Boston is expensive, when it's available. Bostonians drive like maniacs, they're fast, aggressive and view driving as a combat sport (which is why I love it!). If you're staying in town, the T and possibly an occasional taxi will be all you'll need. Bring walkin' shoes.