For casual, you might try Coda, on Columbus Ave around the corner from Back Bay train station. They serve lunch, brunch and dinner and have a great beer selection if that's your thing. Their burger is also really delicious, not on the menu at dinner but always available.
Delux, on Clarendon Street, is a small, totally unassuming spot with delicious grub considering the size of the kitchen and the prices (cash only). I'll highly recommend any taco they're offering as a special, the catfish and pork chops.
Personally I find the slick, prominently located spots in the Back Bay to be mediocre, but admit I haven't been to Tico or Deuxave, mentioned previously. Parrish Cafe is fine but Coda is better.
100 Chandler St, Boston, MA 02116
copley sq/back bay are loaded with restnts.For fine dining I would send you to Erbaluce and Clio and Deuxave, all within a 7-15 min. walk for you. Also, here are some links that may be of interest- that address the bigger boston picture, in case they might be helpful:
Guide to Boston by Areas and Restaurants:
Also, some extra Boston food profile info for you:
shopping for Boston food souvenirs:
La Voile or Bistrot du Midi for fine dining, unless you want very upscale and then L'Espalier might do. Parrish Cafe, Rattlesnake for casual. Tico for tapas and drinks.
774 Boylston St, Boston, MA 02199
261 Newbury Street, Boston, MA 02116
222 Berkeley St, Boston, MA 02116