Not that I've ever been there, but shouldn't NYC be in the top 3?
It makes sense that it's not - it may have a lot of parkland on a per capita basis, but more of that is situated in several enormous parks on the periphery. Where I live (about 20 minutes to midtown by bike or subway), the closest park is about 2 miles away - and those are some traffic-infested, noisy, dirty miles. Not at all a pleasant walk.
The schools are both terrible and awesome - just like everything else here. If you're rich NYC is a wonderful place to raise a family. If you're middle class it's not bad, but difficult. Many people choose to live in New Jersey or just north of the city.
As for crime, it's pretty low. I very very rarely feel unsafe, but I'm a guy. Women would not say the same.
As for sports teams, NYC is home to relatively very few. Yankess, Mets, Cyclones (baseball); Rangers (canadian baseball); now the Jets (urban baseball)... I think that's it? For a city of 9 million, that's pretty much nothing. Consider some other much smaller cities, and how many teams they have - Chicago comes to mind, or even some of the rust belt cities.
What else was on the list? Economics and air quality stuff. Hmm, air quality is not great. Economics - things are great if you're in financial services or tourism or services. Other than that, the unemployment rate is not at all good.
Leisure activities? NYC has very poor access to the water, even though we have a hundred plus miles of coastline within city limits (a city of islands, after all!). This is changing - one of the things Bloomberg will be remembered for. Recreational boating will soon be within reach of people of modest means here, so that's good.
Cost of living is exceptionally high - neck and neck with San Francisco, I believe.
So, yeah - I'm not surprised NYC isn't higher on the list.