Depending how much effort you want to put into riding the subway / taking a taxi:
1) Boston Common and Boston Garden - big open spaces in the center of town. A bit barren in winter but you'll have sightlines and reasonable chances of spotting a red-tailed hawk as well as common birds that are accustomed to people. Lots of people and various holiday lights and activities, which could be a plus or a minus depending on your mood.
2) Arnold Arboretum - A large garden with a great variety of trees and flowers, attracts birds year-round. Hills and vegetation allow for some quiet even though it's a popular spot for tourists and dog-walkers.
3) Mount Auburn Cemetery - like a slightly smaller Arboretum. Great views of downtown from the top of the biggest hill. A hop and a skip away from Harvard Square, but calmingly quiet.
4) Don't forget to check the water's edge wherever you are. Gulls, cormorants, eiders, and many other seabirds can usually be seen from shore, and you may spot a seal too. Inland waters will have a variety of ducks, some geese, swans, and herons, and the occasional osprey.
5) For more ideas, type "Boston, MA" into the top-right search bar here:
https://ebird.org/hotspots Ebird.org is a great resource for birding, especially in the US; you can search for recent sightings of a particular species, check numbers of birds at a particular spot, etc etc.
PS the most reliable way to see a red-tailed hawk is to drive for a while on the highway. They like to perch on those tall lamp-posts. But they're just about everywhere, you just have to keep looking up.
