Statistically, Boston is safer than most cities in the US. And if you avoid the bad neighborhoods of Mattapan, Roxbury, and most of Dorchester, it's extremely safe. Statistically it's comparable to NYC.
I'm not sure how much your husband will be earning so I'm not certain what you're looking for in terms of price. Boston overall is one of the most expensive real estate markets in the country, as I'm sure you know, although if you're used to NYC real estate prices it won't be so much of a shock.
Brookline is a very safe area. It's technically a separate town from Boston but is almost completely surrounded by Boston. It's more urban than an outer suburb of course, but it's got parks and quiet side streets. It's got a good school system and a huge number of restaurants, supermarkets, a great bookstore, restored art deco movie theater that shows independent films, and any other business you could need, in addition to public transit for a short trip downtown and to Cambridge and other places so many people live there without cars. It's not an inexpensive part of Boston, however.
Parts of Cambridge might also have what you're looking for, and Newton is also not far from downtown (a bit of a longer commute to downtown than Brookline, but it's still pretty close in and has public transportation).
Keep in mind the public transportation schedules as well. Public transit is decent in Boston compared to a lot of other cities, but not quite as extensive as NYC. (Although there are parts of Boston where people live without cars - I did it for many years and even now don't regularly use my car to commute).