For such a small area, New England is a surprisingly diverse region; you can do anything from deep-sea fish to leaf-peep on mountaintops, and dine on anything from flapjacks with real maple syrup (at 6am, preferably wearing flannels) to world-class restaurant fare. Yet all five states can be reached in roughly an hour or less by either plane or car from New York City.
As such, it's a wonderful destination for both the family and the peripatetic traveler. In most of the region, crime is almost nonexistent. In fact, your primary worries involve choosing the right time of year to visit; determining the most efficient way to get from point A to point B (New England is still a bit mass-transit challenged); and choosing from among the many natural treasures, roadside diners, and historical tours and walks available here.
