Hi, I hope I'm not too late to answer this!
There are a few places right in the heart of Boston that you might want to look into that have private rooms and good food:
Mamma Maria
Four Seasons
Maggiano's
Lucca
Mistral
Tapeo
State Room
Abe and Louie's
Any of these would do, so I guess it's a matter of cuisine, price, etc.