If you are thinking The Bronx to live then reconsider Washington Heights. That's where I live, the area is gentrifying but still mostly Hispanic with families. The Bronx is only six blocks away. Subway is a block away and 20 minutes from Times Square. And the best part? Rent controlled!
I've lived in NYC for 30 years, just in Manhattan and Brooklyn tho I had girlfriends in Queens and The Bronx so know those places, too. (Stay the fuck AWAY from Staten island tho, nothing but freaks out there.) Where I live now is quiet, calm, affordable, close to the heart of the city and close to my house in NJ so it's perfect. Sure there are drug dealers but it's on the down low as they say. Mostly you see families everywhere.
Parts of Queens can be cool too, and Brooklyn of course but Bklyn is getting expensive too (especially closer to Manhattan) and the further you go out the worse it gets.
So I would pick Washington Heights (which I did), then Queens, then The Bronx.
PS: You see nice cars and SUVs in a bad neighborhood and that's called "stealth wealth". It's where the drug dealers put their money. Everyone in the family gets a 100K SUV, even 90 year old granny. LOL