Central Park is more like a big outdoor garden not in anyway comparable to a large trail system or public lands area. There are trails a little north and in nearby Jersey 1-2 hours by car on the way to (if you head out in the early morning). But on the way back... God have mercy. Expect at least two hours and closer to three and a half in crawling traffic as soon as you get somewhere close to the city.

You can see quite a bit more like the Adirondacks you're willing to drive 5-6 hours, but a drive like that isn't suitable for a day hike.

You can also find some smaller trails and untended areas on the outskirts of the city (eg, Marine Park in southeast Brooklyn). But these tend to be.. well small.

Anyway my point is, like most big cities, it's difficult to really get "outdoors" with any measure of convenience.