Yes, that is a real wild turkey, smack in the middle of Central Park.
Needing a good idea of how to spend a day with the kids last weekend, I hit the net. There always seems to be something going on there, so I figured I'd start there.
I came across the "Amble In The Ramble" free walking tour, and the kids were instantly excited. The tour, which lasted a little longer than an hour, was very informative, and some good exercise. Turns out there are a dozen or so free walking tours which are given rain or shine on a regular basis (except during extreme weather).
So, if you need something to do with the kids on a weekend, check Central Park's website. Upcoming events include a Pumpkin Festival and the haunting of Belvidere Castle on October 25th, just to name a couple.