I think anything around Edgewood Park in New Haven is best right now. East Rock and Wooster Square have gotten super pricey. Lots of brand new apartment buildings in addition to the nice, old apartments. The part of Wooster Square I lived in had way more petty crime and the rent was much higher. Car rifled through if unlocked, packages stolen, and anything outside that wasn’t nailed down vanished.
Edgewood area is a decent trade off; you’re on the grittier side of downtown, away from trendy restaurants and grocery stores, but it’s still really close to downtown and much more affordable. You can get everything you need somewhere on Whalley Avenue, though it is one of the worst streets in the city. There’s a new cycle track on Edgewood Ave that is handy for cyclists. There is some petty crime, varies from block to block, but it’s a population more reflective of the city, so you don’t feel like you’re in a bubble. I prefer that, but some folks might just say it’s louder and less safe. And my pumpkin hasn’t been stolen (yet..).