where is amtrak train station near mccook athletic & exposition (max) center, mccook, cook county, IL?

Answer 1

It's in La Grange Road, at 25 W. Burlington, La Grange Road, IL 60525. Here's a map:
http://stations.amtrak.com/amtrak/DetailedAreaMap.jsp?txtStationID=LAG

Depending on where you want Amtrak to take you, it may be easier to ride Metra from La Grange Park station or someplace, into Union Station and go from there.