Ex New Yorker here.
You got some good advice. I would add that the UWS is really nice, but i would not limit my search to that area: running-wise, if you live within a mile from CP or the west-side park, you'll be fine. I am not a big fan of the UES, it is expensive and kind of dead compared to the UWS, but to each its own.
If you come to NYC for the "experience", then live in Manhattan, or very close to it. If you go to stay in New Jersey, you'll save money and have a nicer apartment, but you may as well stay in Michigan because going to the city outside rush hour is a nightmare.
Finally, don't limit yourself to fancy condos: there are a ton of walk-on townhouses that are nice and more affordable. No need to spend 5K on rent if you don't mind living a bit more frugally. One thing to be mindful about, however, is the noise level. Some areas can be extremely noisy, especially in the night-early hours of the morning: garbage trucks, ambulances, fire-trucks etc.. if you are not used to it and pick a noisy apartment it may drive you crazy. Visit the apartments during the week and make notice of any hospital/fire department/police department/helicopter landing/construction work that may be nearby.
Good luck.
P.S. I know it does not apply to you, but having kids in NYC is actually great. Most of the public schools are between good and excellent, and the social skills they learn in NYC will be incredibly helpful later in life.