I've finally found it! It is exactly the kind of park that I want. It's Meadowbrook Park in Urbana, and it's really close to where I live :-) It has multiple paths, with a long nearly two mile circuit on the border.
It's a prairie restoration park, so the whole thing is covered in tall grasses and sprinkled with nice deciduous trees. One of the paths is a sculpture path, and there's also a wildflower walk. I think when it's a little warmer I will start running there. Since Rachel and I have always enjoyed walking together, I'm definitely going to take her here :-)
I woke up too late for the advanced karate class this morning, oh well. I played some Warcraft 3 instead.