There are no passenger trains which come through Santa Cruz. Instead, the Amtrak-chartered Highway 17 Express can take you over the hill to San Jose, where you can connect to Amtrak trains/buses, San Jose public transit, and Caltrain.
The Union Pacific railroad serves Santa Cruz.
Cave Train Adventure is one of the Boardwalk Rides at the beach. It is a small train that takes passengers through a cave of entertaining diversions.