Freedom Trail. Walk it. Get a guide pamphlet from your hotel or book a bus tour. Walking is best, though.
Paul Revere House.
Old North Church.
Old State House.
Faneuil Hall Market.
Fenway Park.
"The Pru" (Prudential Tower) Observation deck on the 50th floor.
"Plywood Plaza" (John Hancock Tower -- old heads will recognise the plywood reference.) This one is 60 stories.
Boston Common. For what it's worth, you can still graze cattle there -- and they do once a year to preserve the right.
Public Gardens. Ride the Swan Boats.
Aquarium.
Museum of Fine Arts. Go back, you'll need a few days to take it all in.
Science Museum. Don't miss the Hayden Panetarium.
Children's Museum. For kids of ALL ages!
Eat at Durgin Park. Rudest wait-staff on the planet. It's an act, so don't take it personally -- and they take as well as they give. The Indian Pudding is to DIE FOR.
Eat at The No Name Restaurant. Great seafood on the cheap. Seafood chowder is the best in the city known for it. Don't try and find it, just jump a cab from South Station or any downtown hotel.
Eat at Legal Seafood. Local seafood chain, reasonably priced and very good.
Go to The Clam Box in Ipswich, about 30 miles north of Boston. Best fried clams on the planet. Expensive as fast food goes but there are none better anywhere.
Shop on Newbury Street. Lots of interesting boutiques and one-off restaurants.
Eat pizza in the North End. Anywhere will do. Pizzeria Regina on Thacher is worth looking for. There's also on in the Faneuil Marketplace.
And that's just for starters. ;)