$750,000 buys the median home in New York City right now. With 20% down, that's a $150,000 down payment and a $600,000 loan, set against a $70,000 median household income.
Property taxes in New York City run 0.88% of assessed value, below the 1.1% national average. On the median home, that's $6,600 a year, or $550 added to the monthly payment.
New York levies a state income tax on top of the $4,772/month this mortgage runs. Model your real after-tax take-home before deciding how much payment you can carry.
New York City's cost of living index is 187, above the 100 national baseline. That's on top of the housing numbers above, not instead of them.
New York City's median home price runs 285% higher than nearby Buffalo: $195,000 there versus $750,000 here.