I agree about Antioch Park and Shawnee Mission Park. I have always loved Wyandotte County Lake Park as well. It is an older park, and I couldn't tell you much about the play equipment, but even as a little girl I loved going out and driving around the lake. You can almost imagine you're in the Ozarks with some of the views. One new thing they have there that is really cool is the Schlagle Library. It is more of a nature center than a library, and they offer some really cool activities throughout the year, and the staff is fantastic.
And much closer to you would be Ernie Miller Nature Center. It's right on K-7 just south of Santa Fe. They also offer activities through the year, and the staff there is great, too. No play equipment, but lots of trails, and many of them are paved which is great for strollers.