Have you ever been to Palisades park?
You can take the A train to 175th Street, walk across GW bridge, and you'll be in the park.
The trail along the Palisades highway is a bit noisy at times, but the one along the Hudson river is very nice. You can walk around the South end of the park, and take stairs down all the way to the river...then keep going north as far as you wish...every couple of miles there'll be a connector trail that can put you on the high trail, along the higway which will lead you back to the bridge...
Another no-brainer is all the Hudson Valley hikes along the Hudson Line on Metro North around Beacon, Breakneck Ridge and such...
I know you said "outside the city" but, I'm going to take advantage of the fact that most folks in the city don't think of Staten Island as part of the city, anyway, and suggest coming out to the fifth borough!
We really do have some fabulous outdoor spaces, and so many of them connect. If you are into hiking or distance running, I know of a route from the ferry all the way to the beach in Great Kills, 12+ miles of unique trails with fewer than five miles that are on the streets or not alongside a green space.
We have just some cool plant communities that are unique or rare in NY state, too. Birding here is great (though I am no expert). The NY Mycological Society always has a fruitful hunt here.
I'd love to do more to "sell you" on the place, but I'd have to know more about what you're looking for in an outdoors experience.
Once you're here, though, it'll be hard to beat our restaurant scene.