I have gone to Central Park numerous times, but recently I went bike
riding in Central Park for the first time. It was a lot of fun, I
highly recommend it. I think you can easily tour the entire park on
bike. On the weekends, they close the road in Central Park to traffic
so there is a lot of space for pedestrians, roller bladers, and
cyclists to use. You can rent bikes just around the corner from the
park, $20 for 2 hours (10% off if you book online).
One thing to note is that there seems to be a flow of traffic for bike
riding in the park - if you go the wrong way, be prepared to be extra
careful of oncoming traffic!
I could have not imagined more perfect weather to have spent the day outdoors:

There is an area of the park called Strawberry Fields
that is dedicated to John Lennon. It's a very quiet area that seems
like a tranquil spot to wind down and get away from the stress of the
city:

This is one of my favorite spots in the park, Turtle Pond:

If you look by the duck's bill, you will see one of the many turtles
we saw that day. I love coming to to look for their little heads
sticking out of the water as they swim.
There is a lot more to see in the park so be sure to put this on your 'Things to do in NYC' list!