There are a number of 3 star and higher hotels in Back Bay, especially near Copley Square, as well a

Best hotels for Fireworks and Boston Pops Concert on July 4th
There are a number of 3 star and higher hotels in Back Bay, especially near Copley Square, as well as a couple in the Park Square area (on the other side of the Public Garden), and one in Beacon Hill and also the West End - all are about a 10-15 minute walk from the Hatch Shell.
Taj - Back Bay - used to be the Ritz - corner of Arlington and Newbury, over looking the Public Garden - this is about the closest to the Hatch Shell (well, now that I think about it, Beacon Hill Hotel may be almost as close)
A few additional hotels are listed on the Hotels for Boston Fireworks page, including some in Cambridge (5 minute ride away by subway on the T's Red Line). They're slightly farther from the Hatch Shell, but certainly within easy walking distance.
If you book early, it's worth looking for special packages and discount deals. The July 4th holiday usually attracts lots of visitors jerry seinfeld tour schedule to Boston, but there are sometimes some attractive packages available if you book early enough - closer to the holiday, rates rise.
Susan's reply - Hi Paul, thanks so much for the feedback about your experience at the Taj, and very glad to hear it worked well for you. Even without the fireworks and concert, the Taj has a perfect location (it used to be the Ritz until 5-6 years ago) right across from the Public Garden and close to everything.