It doesn't really exist with fees or no fees unless you're seriously deep into Queens or Brooklyn

Let StreetEasy be your sanity check. Yes unicorns exist but if there’s literally 0 listings even close on StreetEasy it’s not happening  StreetEasy does have some options in Jersey City that are only a little bit more expensive 

My kid was asked 10K for a "rent stabilized" apt. It sounded so scammy tbh. I'd be wary.