You could take an Uber from your hotel to Fenway - I always think of Fenway as sort of being the western most part of the city of Boston. That would be probably the shortest distance. You could easily hop the T at Fenway Park from Kenmore Square (Green Line, easy access from Fenway Park, and closer to the rest of Boston than the station marked "Fenway Park") to Park Street (also Green Line, takes you to the eastern end of Boston Common). The basic Freedom Tour starts there, I think. (Note: I've never gone on the tour - this is just the company that popped up when I googled.)
Tours | The Freedom Trail
The Taj Hotel has this quick blog summary of 16 landmarks on the Freedom Trail:
The 16 Landmarks of the Boston Freedom Trail | Taj Boston Hotel
The Freedom Trail goes all over Boston. But I think you wind up at Faneuil Hall/Quincy Market on the "Walk Into History" tour. If you then want to head to the Garden (aka North Station), you could walk north to get to the Garden - it's about 0.75 miles. If you're pooped after a walking tour, or if it's raining, you could take the T from Government Center or Haymarket to North Station, but it might be just as fast to walk.
The Garden's under renovation. I imagine the Pro Shop is open, but I can't be 100% sure. There are definitely no tours of the Garden until at least October, since it's undergoing renovations.