Native New Yorker here. I live in Manhattan and pay way too much for rent. I have a three bedroom in the West Village that I pay $6000 a month. It's true that potential for earnings is higher in the city, but the living expenses usually outpace that. I would try to find something in the Bronx or Brooklyn. You can probably find a decent three bedroom up in Morris Park for $3000. Rent in Brooklyn has dramatically increased in recent years and is slowly catching up to Manhattan. Queens and Staten Island are complete shitholes if you ask me lol
You won't need a car at all. I have two motorcycles, but those are just for pleasure, as almost all my traveling within the city is done through mass transit. So there is some money saved there with no car payment and insurance, but a good portion of that will be rolled over into Metrocards.
This city has almost anything you could ever need or want out of life. And if you can't find it within the city, you are a bus/train ride away from it in either Northern Jersey, Long Island or Upstate New York. There is hiking and nature stuff up in the Catskills which is amazing. If you want to be one of those leafer people, the Hudson Valley area has amazing wineries and apple picking in the Fall. Along with all the shopping you can do in the city, about 45 minutes north of the city is a mall that is probably top 5 in size in the country.
And our bagels and pizza are the best!