Definitely the Westville area of New Haven. There are families of all ages there, parks, a cute little town center with farmers markets, arts fairs and restaurants. Close enough to downtown that you can Uber or drive in but don’t have the hustle of downtown New Haven.

That being said - I currently live in West Haven on the beach and during the summer there is always something going on on the boardwalk but the winters are usually dead (which can be nice as well).