K.R.
The North Kansas City library has an excellend Children's Library with a wonderful storytime. It's a little further for you, but definitely worth checking out. We attend every single week and my kids love it! Airzone was mentioned by another mom and we love that too. I don't know alot about the parks up near you, but we love Macken Park (North Kansas City) and Penguin Park (Vivion and Jackson)
Also, check out Toddler Town at the Sermon Community Center in Independence. (corner of Noland and Truman Rd) The cost is $1/child and the gym is full of ride on toys, Little Tykes equipment, blocks, etc It's MWF from 10-12 every week. Kids can run and play to their heart's content!
My church has a playgroup that meets at a different park/museum/activity every week. If you'd like more info, just send me a message!