Take one of the trolley tours!
They're well worth it. You can make the tour as long or as short as you want since they let you get off and back on again later at points of interest (except for the Duck tours, which don't stop). I've taken a couple of tours when my family visited, and enjoyed each one. You can get tickets & information at South Station.
See this web site for more info:
Fondest memory: My favorite part of living in Boston is taking walks in the Arnold Arboretum. The Arboretum is a treasure! It was designed by the same man who designed Central Park in NYC, Frederick Law Olmstead, and is part of Boston's Emerald Necklace. Mostly you'll find locals walking their dogs (surprisingly, most DO clean up after their pooches) and great specimen trees & shrubs. In the spring and summer, the flowers are lovely. There is also a nice collection of bonzai on display in warmer months. Some of the plants are nearly 300 years old!
For more information on the Arnold Arboretum and Boston's Emerald Necklace, see these web sites:
Please see my Arnold Arboretum Travelogue!
By Public Transportation
Take the Orange Line to the Forest Hills Station. The Arboretum's Forest Hills Gate is a one-block walk northwest along the Arborway from the station.
Refer to the map of the MBTA subway:
You can also take #39 bus to the Monument stop in Jamaica Plain. From there, walk five blocks south along Centre St. to the intersection with the Arborway (Rte. 203). The Hunnewell Building is located inside the Main Gate.