Quincy Market in the city, but Quincy is actually south of Boston. Good news is that its a short (30 min maybe) subway ride from Quincy into the city, or even less time by cab or car ride.
As far as places to shoot...
The Freedom Trail, like Tdragon said, is nice and will take you to many historical points of Boston.
Faneuil Hall is great if you're there on the weekend and want to shoot some street performers.
Boston Public Gardens is good if you like nature, which is also where the pond with the "Swan Boats" are.
Copley Square is great if you want some dramatic wide-angle shots of the John Hancock building.
If you want skyline shots, the best place I'd recommend is anywhere along Memorial Drive, which is a road that borders the north side of the Charles River.
Hope this helps, and enjoy the trip!
Life in the slow lane... 