You can always trade off commute time or access to jobs and culture for lower rent. It’s pointless to complain about more desirable cities being more expensive; if you want to live in a popular area it’s going to cost you more.
I own a newer construction 2Br condo in midtown Atlanta with a 24-hour doorman, pool, dedicated parking, and skyline views and my monthly payment including HOA is about $1300. Brand new 2Br apartments in the building next door start around $1700. Just some more anecdata.
Basically, you have ridiculous standards if you think Prospect Park is crappy, and your price expectations are irrational. Even you admit that your next-door neighbors will be getting roughly the same deal...but they’ll be in Atlanta, not NYC. It’s fine if you don’t like NYC, but you seem to have trouble accepting that a great many people do like it enough to pay more for it.
Also, let’s talk about moving the goalposts: you’re comparing ownership and renting as if they’re the same thing.
In 2011, I rented a 2-bedroom apartment next to the beautiful Prospect park, within a trivial walking distance to 2 subway lines, 30 mins by train to my office in Manhattan, for $1500.
It's not a posh neighborhood, but I don't care.