When I was a very young little girl, (yes, as a matter of fact I did cry when the dinosaurs died) my mom used to take me to a park that offered free rides on a miniature train.
I called her tonight and she let me know that the park STILL exists, she passes it often, and yes, they still give free rides on occasion. They have some kind of deal with the city that they can use the land, in exchange for the free rides to the public.
Here is a webpage that shows images of the trains. *sniff* Aren't they beautiful?
The official website.
*thinking I really must do something extra special for Mom on Mother's Day this year*