Greetings Lisa:
I would probably start by asking local park staff to determine if they can quickly point you to a mockernut hickory tree in close proximity to your residence. Park staff include both municipal and state parks.
Alternatively, you can try contacting a regional IL Dept. of Natural Resources district forester, heritage biologist, or wildlife biologist who can steer you to a local park that has a population of mockernut hickory.
http://dnr.state.il.us/orc/
Best of luck!