The Fanueil Hall area will satisfy everyone in your family. Restaurants, shopping, activites for the kids, and historical sites all highlight the area.
Many will say that Boston is a walking town to begin with. That's true, but with that said, there's still a lot crammed into the area around Fanueil Hall. The marketplace is situated in three old warehouse buildings (think of small versions of the warehouse at Camden Yards) and offers various shops from mall staples such as Discovery Channel, Banana Republic and Sam Goody's to small art galleries. The center building is almost solely a food court, offering things from seafood to bagels to pizza to chinese to pastries. The outer walkways (new glass extentions to the historic old stone warehouse) of the center building is lined with carts selling toys and chatzkahs.
The market area also has a number of sit-down eateries and bars for nightlife. The Rack is an upscale billiards hall and bar, The Comedy Connection, Froggies and Pizzeria Uno's all add to the night life. The best of these places though is Durgin Park, a restaurant that's been there pretty much forever and has the reputation to boot.
Between the buildings there are often many street entertainers around. Magicians, musicians, and Ben Franklin (why he's here and not in Philly, I can't tell you) are those that can be found most often.
Just a short walk under and past I-93 is the New England Aquarium. Of the aquariums I've been to around the world, this is my favorite. The large layout with a penguin pool at the bottom and a large circular reef/shark tank in the middle offers a lot to see. The aquarium (as the other boatlines that line the Long Wharf) offers seasonal whale watching trips. Sightseeing cruises around the harbor and to some of the islands are fun and are available from the wharf opposite the aquarium.