My guess (based on many stays in Boston, not anything particular about what the NCAA has reserved for this region) would be that they'd be staying in the Prudential Center/Back Bay area. If you have any kind of points program with any hotel chain, they'll have a building there. If you don't, I stay at The Colonnade a lot, which is in that area. They're about three miles from TD Garden. There are closer places, including a CitizenM right (cool if you don't mind a small room) next to TD Garden. There's also the Marriott Longwharf on the Harbor, which is about a mile walk from TD Garden. It's next to Faneuil Hall and the Aquarium, so there's also stuff to do there.
However, I do think the Pru Center area is most likely, in part because the Pru Center itself is a large mall with lots of restaurants where teams could walk to. There's also an observation deck at the top, which seems like a possible between-day activity.
Also, TD Garden is close enough to the North End that you can have a great Italian meal and walk to the arena.