Boston is a big city, yet it is possible to see all of the famous sights in one hour at one place: the Skywalk Observatory, inside the Prudential center. As a local, I go there often to see how the city and the view changes—spring's vivid color, summer's blue, fall's orange and red, and winter's white. One side faces Fenway Park, another side faces Harvard and MIT, and a further view looks out over the airport.
Think that's all? Not quite! A couple of floors down you can have a nice dinner with the view—even just for a drink or dessert at night, surrounded by the city nights. (Not to mention the massive shopping areas downstairs.)
If you stay one of the hotels nearby, you really don't have to go outdoors at all on a rainy day—you can still see it all!