If you have time, try the Isabella Stewart Gardner museum - it's a gem.
There are 3 "burying grounds" on the Freedom Trail, and I love going by all of them, although I think Granary is my favorite. (Of course, that's only if you like visiting historic cemeteries.)
Try visiting the North End; eat Italian, but try to manage to save room and go to one of various pastry shops. (Or just skip dinner and pig out on cannoli and marzipan. . .)
I haven't been to the Harvard Museum of Natural History in about 12 years, but it's on my list to visit the next time I go. It's an amazing place.
It depends on how many days you have, but I'd try to get out to Salem and just meander, with the thought in mind that you might try to hit The House of the Seven Gables, maybe, and definitely just enjoy the funky vibe of the place. (If you like Indian, there's a great place close to the statue of Elizabeth Montegomery,btw.)
You might also take the National Parks Ferry out to Georges Island to see Ft. Warren. (Something else I haven't done in about a decade and would like to do!) Or maybe take a whale watching tour, those are fun.
Spend some time meandering Newbury Street. It's a blast, but lock up your credit card, otherwise, oh my, it's easy to be bad on Newbury Street. . .
I've had fun just meandering in Cambridge as well, although I know where there's a great Ethiopian restaurant and a couple of nicer thrifts, so that helps, LOL.
There's just so much to do in Boston! I can think of many other things, but they're mainly v.v. history heavy (Plimoth Plantation, any one of several house museums etc.) because that's what I'm into.
As for a hotel, I think I'd find something in Newton, Cambridge or Brookline close to a T stop and do that rather than staying IN Boston. Just me, although, if I ever stayed in Boston, it would have to be at the Parker - it's supposedly haunted and they will give you one of the "haunted" rooms if you ask for it.
Hmm, on that note, there's a haunted room at the Wayside Inn in Sudbury (the one in the Longfellow poem) that is great, great fun. You can go by Concord and see Alcott's home and visit Walden pond and do the whole Concord poets touristing then follow up with the Concord and Lexington history.
Okay, I've rambled long enough. . .now you've got me planning my next trip up that way!