Gitchigumee:
You are right about not knowing what is right in our own back yards sometimes!
Pilcher Park and the Barber Horticulture Center kind of come to mind. I know that my husband and I have run a 5K race out at that park before and it was really beautiful. Here is a link to the Joliet park district's site:
http://www.jolietpark.org/Facilities/index.php
Here is also a link for the Forest Preserve District in the area.
http://www.fpdwc.org/sitemap.cfm
I go to the Rock Run Preserve (scroll down a ways to see the various preserves listed) only because it is very close to my house. I know that the paths are very well maintained.
Hope some of this helps!