Congratulations and best of luck with the move. My first piece of advice is to carefully reconsider buying a home until you have lived here for at least a couple years. New Haven and the surrounding towns all have neighborhoods that will probably meet all your needs. You need to get to know the area to find the area that suits your specific needs. Don't rely on a real estate agent or, even worse, a bunch of opinionated strangers!

Safe neighborhoods are not hard to find in New Haven and elsewhere. I let my kids walk and bike all over the place without supervision. They walk to friends' houses, stop for a soda, etc. There are plenty of good schools to choose from. This is Connecticut, not Alabama. You will be fine.