Badger Creek State Recreation Area is a popular fishing destination, with a large lake. There are no designated trails but there is wooded space to explore as well. Every year in mid-July, there is a large sunflower field that is popular for taking pictures (details below for the 2017 field location).
Island Park feels more like a campground, with a playground in the middle, I don’t think I’d go back just to play. The river running nearby has a metal bridge going over and you can see the dam.
Kinnick/Feller Park is large and shady, with several sports fields, a playground, and a river running nearby.