If you've driven down Hayden, you may have noticed the dog park on the north side of this park, at McDonald. There always seem to be a lot of dogs leaping and running around in the large fenced off-leash areas.
South of the dog park are several large sports fields. When you come to Jackrabbit Road, there's another parking lot. This is the closest parking area to the swimming pool and the playground. There's also a basketball court area.
The playground is shaded and very fun for kids of all ages. It has a little zip-line for kids that were a hit in my family.
And of course, there is the long lake (artificial of course) with the walking path around it. The lake goes all the way (almost) to Chaparral Road, so it's a good place for some exercise. Or just a nice walk. You can even go fishing in the lake if you have the proper permit (kids can fish without a permit, I think).
The path around the lake, the dog park, the playground...
The dog park is at something of a distance from the lake.
McCormick Stillman Park (the "train park") is great for kids (at Indian Bend and Scottsdale Road).