There are a couple of different tour buses that give you a chance to get off and on in various spots, not sure if they have stops at S Station. But, you could ride around until your time budget is up then pick up a taxi to Logan.
A little thinking off the top of my head here...
Though Boston is generally walking friendly, the area around South station isn't so much, and the financial district which is what is right around there isn't so interesting (IMHO).
Anther possibiity might be to get the subway to someplace like the downtown crossing stop, that would get you closer to some of the interesting areas for walking. You'd be able to pick up some of the Freedom Trail and catch a few of the landmark buildings and graveyards where some notables are buried.
You could also stroll around Beacon Hill which has some good photographic possibilities (not to say that the rest of town doesn't).
Some links;
Dead Link Removed
http://www.mbta.com/
http://www.bostonducktours.com/
http://bostonwatertransportation.com/watertaxis.html
I'm sure some of the other North Easter's will chime in.
If it's raining there's aways some of the museums, or the Navy Yard and the USS Constitution perhaps.
The aquarium is not very far from South Station, as I recall.
OTH, 2 hours is not much time, how much it really is depends on your flight time, it can take 15 minutes to get from downtown to Logan or it can take an hour +
Another idea... take a walk from S station and catch the water taxi to Logan.