The
New England Aquarium is at the top of the list: indoors (important in December), has an IMAX theater, great for kids, advance tickets available, and about a 5-minute walk from your hotel.
If the weather is nice and you've got the right clothing to be outdoors, the
Freedom Trail passes through the Faneuil Hall area and is chock-full of important historical sites. No charge for walking the Freedom Trail, though some individual sites might have an entrance fee (probably not available in advance) to get inside.