My daughter has lived in Boston now for a dozen years. The areas you are mentioning are very safe. My only warning is to keep in mind when riding the T that it is not 24 hours. If your kids are out late and need to catch the T to get home, they should make sure they start their trip home before the last T.
And yes, it is a city and you need to be aware. If somebody in your train car is acting weird you move to another car, if a person approaches you asking for money you keep walking and don’t make eye contact, etc.