> Offhand, I can't think of any 'park and ride' style Car <> Transit (train or not) interface in the USA that _does_ charge anything to park there.
Many of the lots at train stations in the Chicago suburbs charge fees to park for the day, usually a couple bucks, and there are annual parking passes that you have to wait years to get at some of the stations (I think Naperville is a 5+ year waiting list at this point).
However, all of the park n'rides for buses in the suburbs, at least those that I'm aware of, have free parking. And at least in my experience there's usually enough parking spaces for everyone who's taking a bus.
But the train system is much more desirable than the bus system here, so the demand for parking there is much higher. I live in a suburb that's like 25 minutes from all train stations, so I take the bus from a park n'ride just a few minutes from me, when it's on time it's pretty great, but it's not super reliable...I had to wait an hour at the bus stop downtown last Friday before my bus showed up (with another one for the same route directly behind it, they got that backed up) and once I was on it took an extra 30 minutes just to drive down one street in downtown Chicago, the traffic was so bad.
EDIT: While double-checking a few things, I discovered that Naperville is getting rid of its parking permits this fall and going to daily fees only[1].
[1]: https://www.naperville.il.us/about-naperville/transportation...