Kuwana is connected to Nagoya by two competing lines.
From Tokyo, allow 2hrs 20mins and ¥11,510 (via the JR Kansai Line) or ¥11,730 (via Kintetsu) (slightly longer and cheaper if avoiding Nozomi trains).
Kintetsu runs one direct Limited Express per hour from Osaka-Namba, taking just over 2 hours and costing ¥3730 (about 30 minutes longer than taking the Shinkansen and going through Nagoya, but roughly half the price). Alternatively, you can take a Limited Express to Ise-Nakagawa or Tsu and change there for a train to Kuwana. If you want to take Kintetsu from Osaka but avoid Limited Expresses, it will take about 3hrs 20mins but cost only ¥2120.
Kuwana is also served by the JR Nanki Limited Express four times a day. From Nagoya this is no faster than the JR Rapid trains, and at ¥1820 is far more expensive than any other train; in the other direction, however, it serves Owase, Kumano, Shingū, and Kii-Katsuura (about 3 hrs 20 mins and ¥7050 from the latter). The JR Mie Rapid trains compete with Kintetsu on the route to Ise and Toba, which is roughly 1hr 30mins away.
(Note that between Yokkaichi and Tsu, Nanki Limited Express and Mie Rapid trains run on the non-JR Ise Railway. If you are using a Japan Rail Pass, you must pay a surcharge of ¥510 for Mie trains and ¥820 for Nanki trains.)
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