Newark airport is much easier to navigate but taking the train from JFK is also easy. Once you arrive at the terminal there are many hotels within easy walking distance. Avoid laGuardia.
The Times Square area is great with easy access to theater, the subway and tons of restaurants. Don't be afraid of the subway. It's relatively clean and safe. And you can get everywhere.
My favorite museums are the metropolitan...the subway goes right to it..,and the Frick, just a couple blocks away. The Guggenheim is also very cool.
NY is made for walking. Don't try to get too much in. Stroll around, watch people, take a buggy ride thru Central Park, see the Statue of Liberty, take a boat ride around the island
We live in Chicago but love ny for short visits.