Must see's

Freedom trail
Boston Common, the State House, Park Street Church, Granary Burying Ground, King's Chapel, the Old State House, the site of the Boston Massacre, Faneuil Hall, Paul Revere's House, Copp's Hill Burying Ground, Bunker Hill Monument and the USS Constitution.
Museums
Museum of Fine Arts
Museum of Science
JFK Library and Museum
Isabella Stewart Gardner Museum
Institute of Contemporary Art
Gibson House Museum
USS Constitution Museum
MIT museum
Misc.
Harvard
Fenway Park
Boston Commons + Public Gardens
Prudential Skywalk
Holocaust Memorial
Boat / tours
Boston Duck Tours
Beantown Trolley Tour
Whale watch
Constitution Cruise (Boston Harbor)
Boston Tea Party Ship & Museum
Salem
Hous of the 7 gables, Peabody Essex museum, witch museum

If time allows

New England Aquarium
Mapparium at the Mary Baker Eddy Library
New England Sports Museum
Harvard Museum of Natural History
The Harrison Otis House Museum
Nichols House Museum

Shopping time

Faneuil Hall