Greetings Laura:
With a little bit of persistence, I'm confident that you will be able to find a bur oak acorn out in a nearby forest, park, cemetery, etc.--it may not be the prettiest acorn or acorn cup, but it should help with the 4-H poster project. Make sure to look under the leaf litter :-)
Alternatively, you may try to contact a local nature preserve/center with the Peoria Park District.
Good luck and good "acorn" hunting!