I want to hold my son's first birthday party in Central Park and I was wondering what the best place would be (west side pref.). I want to stay away from the playgrounds if possible.
Where in Central Park are there picnic tables? It would be easier to set up around them...

There aren't picnic tables in the park. You can bring your own portable tables, but it's easier to bring a bunch of blankets and find yourself a nice piece of grass.

Sheep's Meadow is ideal for small parties and social gatherings. It's located around the West 67th Street entrance, and Tavern on the Green.