There are ride on/ride off bikes all over the city -think you download an app and with Lime Bikes, especially, you can leave them absolutely anywhere once you are finished. Public transportation is pretty good for the places tourists will be going.
I would do:
Freedom trail - there are guides who will help you and a literal red line to follow from beacon hill to north end etc. - see Paul Revere's house in the north end have cannoli. depending on the weekend there will probably be a saint's festival in the north end.
Black Freedom Trail - fascinating.
Newbury Street/comm ave for shopping and walking. There is also a house museum on Comm Ave (possibly Beacon Street) which is an authentic untouched early 19th century house - fascinating if you are into that kind of thing. google
Chinatown is interesting - great dim sum
Cambridge is lovely just to wander through Harvard Yard. Harvard art museum is lovely. Widener Library is lovely and I think main bits are open to the public. Students start going back around the end of August.
Isabella Stewart Gardner and MFA are close by and are wonderful - fab american art exhibition that is relatively new.
If you are into books, do a tour of the Boston Athenaeum - it is right by the state house.
You often get broadway shows in Boston - google the Boston Opera House - think Book of Mormon is playing soon. Cirque du Soleil is also in town. Also some decent theatre here - American Repertory Theater in Harvard Square is excellent.
Concord/Lexington are nice to visit if you have a car (although Concord is actually on the train line). Classic new england towns with loads of revolutionary war connections plus Walden Pond is lovely - near Concord. IF you liked Little Women, Louisa May Alcott's house in Concord is really authentic and interesting.
Walking along the Charles River esplanade is lovely. There are places you can hire kayaks too.
Aquarium and Whale Watching - leaves from near the aquarium.
I would definitely do a day trip to Provincetown. The ferry is lovely and the town itself is amazing - especially at the height of summer.
Boston Public Library has a charming courtyard and some lovely Sargeant murals.