I love living in NYC, but if I had to go to JFK or LaGuardia twice a week, I might off myself. They are not convenient airports for frequent commutes. JFK is about 90 minutes each way on transit or a ~$50 taxi ride for me; I live in Manhattan near the upper end of Central Park. I don't know if there's a suburb that they are convenient to... New Jersey you have to drive through NYC to get there; Connecticut and Westchester is a minimum 30 miles of driving to get there. Maybe you're OK with that, I don't know - it would depend a lot on what time of day you were driving, rush hour commutes of that length could be awful. If you were flying on weekend days, not so bad.
Reading your post I don't see a lot of reasons to move to NYC. What appeals to you about it? Have you ever visited? There's a little "city life without a car sounds good" in your post, but that's about it. You could get that in a lot of places, and many of them would be better for you with easier access to airports and outdoorsy activities. I used to live in Cambridge, Mass. and it would be right up your alley - easy access to airport/train, great (but laid-back) restaurant/cafe/cocktail scene, good transit, super safe, very walkable, very bikable, easy to get a car and head out of town for skiing or hiking day trips or weekend trips. New York isn't that place, it's hustle and bustle and crowds and noise. I love it because I like people and I like the attitude of New Yorkers and how open they are to strangers, and I love how New York has such unique opportunities to experience culture (music, museums, film, street festivals, food and culture from everywhere in the world, etc.).
If I were you I would need a lot of "I am dying to live in NYC to experience X Y and Z" before I would be willing to put up with the airport commutes... maybe it's there, but I am not hearing it in your post.