I would definitely recommend just walking around. Boston is a great walking city!
The Freedom Trail is a great way to see Boston's most historical sites.
Or you can easily spend half a day wandering around Back Bay, Boston Common, or Faneuil Hall, more touristy but still really scenic.
Rainy day plan: museums! There's the Museum of Fine Arts, Isabella Stewart Gardner Museum (I definitely recommend this one), Institute of Contemporary Art, Museum of Science, New England Aquarium, Mapparium (also cool), and tons of other small museums.
There's so much! Brewery tours, Harvard Square, Arnold Arboretum. I recommend more than half a day if you can swing it! (but I may be biased being from Boston..) about 8 years ago
Definitely go on a duck tour!!! It leaves from right next to the Boston museum of Science and travels down the streets. Then it turns into a boat and goes for a ride in the water! The ride is a nice length and there are AMAZING details by the tour guide about the city the entire time. Google it for more info:) almost 8 years ago