Parking near Central park?

Yes. Sometimes

Plenty available and at your desired rates and locations. Just download SpotHero parking app. I parked right on 5th avenue for an entire day for around USD 40 plus taxes. And the parking usually extends all night for free. Bigger cars have extra USD 10 or so charges. Of course, the farther from the park, the cheaper it gets. But I was right outside the park on the east side. Again, it's your choice based on how much you want to spend and walk. :)