Regarding health insurance, this will likely come from your employer and costs vary wildly. Ask to see the Healthcare plan costs (which you’ll pay per month just to have the insurance) and explanation of benefits. Most Healthcare plans have a deductible, and you’ll need to pay that entire amount out of pocket before the insurance pays anything. Then you’ll have a copay or coinsurance until you reach your maximum out of pocket. As a best practice, always assume that you’ll reach your maximum out of pocket amount each year when budgeting.
I’ve never been to NYC, but I live in a nearby state and ran a cost of living comparison report. My salary is close to yours in terms of comparison. It allows a middle class lifestyle - middle of the road housing, transportation, takeout once or twice a week, some hobbies, vacation once a year. I don’t have a family so you may need to be a bit more frugal.
It’s crucial to have a nest egg set aside in case you lose your job because social services are minimal. Also bear in mind that most US jobs don’t offer a pension, but instead your job likely offers a 401k or IRA. That’s usually not enough to retire on, especially if you plan on renting, so try to budget for investments if you ever plan on retiring.