One of the Summer Shack locations is right next to the OP's hotel. I'm not a big fan of the place, but some people are. (Jasper White was an executive chef at Legal Seafood's back in the '70s when it was THE hote place to go for seafood.) If you do go, I think their signature wood grilled lobster is the best thing on the menu.

Sonsie's is an easy walk from the hotel and has the advantage of offering an open front onto Newbury Street, so it's a popular place to go for those who want to watch all the Newbury Street action. I've heard they have decent food, but I haven't been in years.

Kingfish Hall is part of the Todd English empire and is in the Fanueil Hall complex, both of which make it suspect for me.