NYC has in the past pushed state laws that just affect NYC. Gun laws in particular I'm more familiar with [state preemption - except for NYC where they can enact their own gun laws], but some taxing is specially allowed for NYC too. It's not unheard of for state-level legislators (from NYC) to push for something to the state either because 1) the state constitution doesn't allow a city to do XYZ, or 2) because the city government doesn't see eye to eye with the state representatives living there

New York City has very little direct authority, most (not all) City legislation must be passed separately by the State legislature and signed by the Governor to be effective law.

For example, the City had to request the State to lower the speed limit on City streets to 25 mph from 30 mph last year.