The Athens of America
As with any large city, there is the presence of crime in Boston, but for a place of its size and population, it is below average. Downtown Boston is relatively safe and some of its residents even leave their doors and cars unlocked (this is not recommended for visitors though, just to be safe).
As with any city, it is not advisable to walk down dark alleys at night, but walking down the main roads should cause you no problems whatsoever. There are some gang areas just outside Boston, in places such as Roxbury, Mattapan and Dorchester, but steering clear of such places will see you have a pleasant and uninterrupted stay.