Definitely the essex house or the ritz central park. Both are right next to each other (just about, like 3 doors down) but both open up right onto the park. Be aware the central park view rooms come at a pretty substantial price difference, so if you can, maybe try to secure an upgrade to one before your stay, otherwise (like many places in NYC) you might end up staring at a wall out of your window.
The essex house is wonderful, and I was offered an upgrade to the JW terrace suite there (with a nice balcony, some of which overlook central park, so ask) for $200 a night on an award stay. Not bad considering the rack rate when I stayed was $5,500 a night. If you have a Ritz card, it the ritz central park could be a great use of club level upgrade certificates. Rates for the club level upgrade certs are the standard rate (which is about $40 more than AAA rate) so depending on how much you're willing to spend it could be a good deal.