Here's the link to the Johnson County parks:
http://www.jcprd.com/parks_facilities/directory.cfm
Overland Park also has many great parks, and the website is pretty helpful. Plus, if you have any questions, just use the contact link and ask someone! They've been great for me (as have the people at Leawood's parks page.)
http://www.opkansas.org/_Res/Parks_and_Recreation/index.cfm
There are tons of wonderful parks much closer than Swope, and much safer, too. Good luck, and enjoy! My son really enjoys Antioch Park (Shawnee Mission & Antioch), Leawood City Park (105th & Lee), South Lake Park (87th just east of Antioch), and of course, Deanna Rose (an Overland Park city park, at 137th & Switzer, with farm animals, hayrides, playgrounds, etc. WONDERFUL park!).