The subway is great. You have to buy a card (for something like a dollar), and then you can recharge it over and over. If you want to save the dollar, often you'll find a used card just laying on the ground on the stairs or just inside. Don't know why people toss them, but they do. We actually found two or three.

I can't speak for the routes (e.g. Yankee stadium), but I remember it being pretty easy to get around.

There was a fair amount of walking, but we visited the Intrepid, WTC memorial park, Chinatown, John Lennon's former residence (by the Park, so we also walked through Central Park), did the free ferry to Staten Island (which gives you a great view of the Statue of Liberty), and a few other things. No issues in the Park during the day.