How about Longwood/Mission Hill/Hyde Square area? Close to the orange line for the Backbay Station T stop, and Jamaica Pond to walk and cycle. Nice area.

Or perhaps JP. More funky and sometime a bit dicey but a lot cheaper and tons of shops and restaurants. Also on the orange line. And next door the Arnold Arboretum and Franklin Park. The area east of Centre street and just west of the Green street T stop is pretty nice to live. Walk to Centre st. for the shops and restaurants.