Just fyi, OP - most of the towns recommended here have high housing costs. If you’re looking to rent, be aware that these towns consist of mostly single family homes with low density zoning, and there aren’t many apartments. Also factor in commute and cost of parking. Indeed, these are some of the best districts in the state, but also CT has some of the best public schools in the country, and most districts offer a very good education.

If you’re looking to stay close to campus, then East Rock has tons of young families. Many are Yale-affiliated. It’s nice to be able to walk your kid to school and then walk or take the free shuttle/bus to work. Westville is also popular with families. It’s a little farther from Yale, but New Haven is a very small city, so it’s not a long commute, with a couple of bus lines if you don’t want to pay for parking.