Take them on a walking tour of The Boston Common and Beacon hill. Given this is MMM you may not be inclined for this but there are outfits that will give you a guided tour.
Take a walking tour of the North end (basically our version of little italy). Paul reveres house and the old north church are here. Grab a canolli at mike's pastry, pizza at reginas pizzeria
The Museum of Fine Arts and Isabelle Steward Gardener (both art museums) are basically right next to eachother, easy public transit.
Go to Castle Island in South Boston, get some ice cream at sullivan's, walk around the park / castle get here via bus from downtown in no time flat.
Take the Ferry to Boston Harbor islands, great views of the city, on island museum about the history of the islands.
Science musuem and aqurium are of course great, natural history museum too. The kennedy museum is in my opinion a real snoozefest unless you are a major history buff.
Go to the arnold arboretum, beautiful trees, olmstead park, free.
Rent bikes and ride along the charles river in cambridge.
Get seafood - I would suggest: Belle Isle seafood in winthrop, Tonys Clam shop in Quincy.
There is a Hostel (Hostelling International) on Hemenway in the Back Bay. Two years ago when I was moving here I stayed there, private rooms were in the ~100 range, and you are /right/ on the green line. (Hynes convention center stop)