The steepest (and highest) hills in NYC proper are on Staten Island, which happens to have some pretty decent riding in general. Starting and ending with a ferry ride is a bonus.

Otherwise the closest decent climbs are in Northern NJ starting 10-20 miles NW of the GW bridge. Westchester is also hilly, but decent climbs are all North of White Plains, with higher hills about 40 miles from NYC.

One bonus if you want to ride in Westchester is that you can get a bike pass for Metro North trains, which allow you to bring the bike on board any non rush hour train. So you can leave Grand Central Station and be in North White Plains, which most locals consider the gateway to decent riding here. For bnicer riding you might start farther north ie. Katonah or Goldens Bridge. One nice way to ride in Westchester is to head north form a start in the middle of the county, then loop west and take the train home form somewhere on the Hudson.

Lastly there's excellent steep hill climbing in Connecticutt, just North of Westchester County airport. Or you can ride the rails all the way to Poughkeepsie and explore either the Catskills, or the Central Valley.