What can I say, we love Nature Centers! Ernie Miller was Johnson County's first Nature Center and I think it is probably their best.
The park has great trails for hiking, bird watching, animal track identification, and enjoying nature. My son and husband go nearly every weekend in the summer.
The Center has displays and exhibits and live animals for the kids to check out and they host all sorts of events year round. My favorites are Laura's Legacy (about Laura Ingalls Wilder) and Escape to Freedom (about the Underground Railroad). These programs are geared towards kids, usually age 6 and up.
They also offer preschool events throughout the year and several open to all ages events so the whole family can enjoy it. Most of these events require pre-registration and some have small fee as well. Check their website for events and fees each year.
They also offer camps during school breaks for all ages.