Natick is quite safe.

One thing you can do if you're totally unfamiliar with a given area is check the local police logs. You can get a sense of how active the cops are, what types of crimes are most common, where they're happening, etc.

I live in one of the safest towns, statistically speaking, in MA. Out of curiosity, I checked the police logs when we moved here and there were literally entries like, "Homeowner called to report a suspicious fox on edge of property. Officer responded. Did not find the fox," and my recent favorite, "Local resident reporting they were victim of an internet scam involving an XBox."