Copley Plaza Hotel is elegant "Old Boston" in Back Bay - great shopping (Newbury Street, Copley Place), Public Garden, Beacon Hill, Charles River and Boston Common all easily walked to.
Four Seasons is - well, Four Seasons - on Public Garden, near everything as well.
Raj is the original Ritz Carlton, smaller rooms, but equally elegant and near all the above mentioned sights, right smack on Newbury Street across from Public Garden.
The Liberty Hotel is at the foot of Beacon Hill on Charles River,close to the "T" and a funky, cool hotel - closer to waterfront sights and north end than the others. Used to be the Suffold County jail building, historic and great views from the rooms.
The Boston Harbour Hotel is right on water, great views from harbor side rooms. Elegant hotel. Near Fanueil Hall and North End. I think it's a little more "touristy"in that area in summertime - but if you like the harbor setting it cannot be beat.
Definitely stroll through North End, window shop and people watch on Newbury Street, wander around Beacon Hill and ride Swan Boats in Public Garden. Take a harbour cruise. Walk along the Charles River, maybe see a concert on the esplanade. Harvard Square and the Harvard Museums (Natural History) are very nice. The Museum of Fine Arts is spectacular. Go to top of Prudential Building for the views. Aquarium is nice. The "Duck Tours" are great for kids. The Museum of Science is great. Skip Fanueil Hall - just the same stores you see at the mall and crowded -maybe walk through on your way to North End to see Old orth Church and maybe catch an Italian street festival.....