There are so many wonderful parts of Central Park it is hard to chose a favorite but the Jacqueline Kennedy Onassis Reservoir gets my vote. Though no longer serving as a water supply for the city, this reservoir stretches from 86th street to 96th street and is a beautiful place to escape the bustle of the city. With a 1.5 mile jogging track around the perimeter, this is a very popular place for locals to go running. You are also guaranteed to see a variety of wildlife from ducks to loons and maybe even a turtle if you are lucky! In the spring the track is lined with pink Yoshino Cherry blossoms which is absolutely worth seeing.
If you are planning to visit any of the big museums on the Upper East Side, I would highly recommend walking through here before or after your visit. If you are coming from the Upper West Side, this is a great way to walk across the park and end up right outside the Guggenheim. If you exit the jogging track on the East side of park you will be right outside the entrance. Then just a few blocks down is The Metropolitan Museum of Art! It makes for a great way to see some nature and culture all in one day!