We needed a spot near Mammoth Cave National Park (which was full). This small City Park in the town of Munfordville, only 25 miles away, fit the bill perfectly. The phone number connects you to their City Hall - they asked for the make, model, color and license plate number of our vehicle (so their police officer would know we belonged there), and told us spots are available on a "first come" basis but are almost always available. In our case, we were the only ones there on a Friday summer night.
The park is delightful: it's by a river, surrounded by trees, and has a paved path circling soccer and disc golf fields, a playground, and four pickleball courts. There also is a 4-mile trail. All of the day users left by 9 pm, and then we had the park to ourselves. It was a very quiet spot.
Access to the park is via a short one-lane road that has some very tight curves. The overnight spots aren't really set up for RVs - those also are accessed via tight turns and there isn't an adequate turnaround space at the end of the access road -- I parked in a spot knowing that I would have to back my 23' trailer down the access road in order to get to back to a larger parking lot area. For smaller RVs and trailers, camping here is manageable and recommended.