South Station, Boston MA?

Yes they do. I have taken the bus to NYC a few times both Grey hound and mega bus and they leave at South Station. Grey hound's bus stop in the south station bus terminal is on your right right after you walk into the long all way. You will see ticket booths on the left and right and inbetween is a hall way that takes you to the bus terminals and the first one on the right is grey hound to NYC and all the way to back and to the right is MegaBus and Fung Wah bus to NYC and also the Lucky Star bus to NYC. Fung Wah is no longer in service though.

Many do, but I know there's at least one other that goes between Boston's and New York's Chinatowns, and it's pretty cheap.

There may be really nothing close to South Station however the monetary district, however getting around on the T is low-cost, and you could get day passes. There is the Science Museum, the Museum of best Arts, the new England Aquarium, the Boston Public Library, and Quincy Market, Copley situation and Newbury avenue for looking (despite the fact that simply window shopping), for starters. If you are a history buff and don't intellect being open air, are attempting walking the freedom trail.