I've actually driven there for a rail fan trip. While there is plenty of parking it is not separately identified as to long term or short term. I suggest asking ticket agent and letting them know you will be leaving your car there while traveling. I've actually become friends with Maury G who runs the museum. When I made a day trip from Chicago to Galesburg this past October just to visit with him, he told me the museum is closed during the winter and was not open the day I visited but he took me inside anyway to show me the changes they had made since my first visit in 2014. As for the very large parking lot, I am not aware of what security they maintain but as I said above, I would let the ticket agent know I was leaving a car.