I love Boston- I just wish it were cheaper to live in the area!
There are several excellent restaurants in Chinatown (Chinatown or NE Medical Center T stop.) We like King Fung Garden, East Ocean City and Pho Pasteur. Montien and Penang are also good.
In the North End, you should really try both Mike’s Pastry and Modern Pastry and decide which you prefer…
We like Neptune Oyster, Giorgio’s, Strega, the original Pizzeria Regina, and Antico Forno.
LOTS of good bars and pubs- the Asgard or Kinsale, The Burren and Jacob Wirth come immediately to mind. As for markets- just explore! There are great markets everywhere throughout the city and many have take out as well.