Mie Precture is a wonderful place to ride trains in Japan. One of the most scenic is the Meishosen of JR Tokai that runs between Matsusaka and Ise-Okitsu. The line is narrow gauge - 3 foot 6 inch gauge - and runs diesel railcars in two car sets. The line starts out in the flat plane in Matsusaka and runs into the mountains crossing bridges and passing through numerous tunnels. Its a mountain railroader's delight. After your trip, be sure to try some Matsusaka beef for dinner!
The Kintetsu Railway, which is a modern standard gauge passenger hauler, has lines down to Mie's seaside resort towns like Toba and Kashikojima. These towns and others like them are paradise and offer all sorts of sightseeing opportunities as well as delicious seafood that is out of this world!