Yes, I have many friends (10ish maybe) who aren't natives but currently live in Brooklyn. Queens is affordable too (you can buy a small house for ~$300,000ish IIRC, I think in Rockaway Beach) but you're very far away from Manhattan. I had another friend who lives in Long Island City (Queens, close to Manhattan) but her rent was high IIRC. I'm unfamiliar with the rent in The Bronx.

However NYC as a whole has high sales and income taxes though. Including City income tax.

Brooklyn is where you live when you move to The City without a lot of money - like for grad school.

Rent is (probably) higher in Park Slope or Williamsburg though which are more "desirable" areas of Brooklyn.

I'm sure natives can chime in.