Take Kintetsu line from Osaka to Kuwana. First you have to get to Tsuruhashi station and change trains for Kintetsu line. Take an express train bound for Ujiyamada and change trains at Isenakagawa and take the express train bound for Nagoya. Train charge is 2,240 yen for adult from JR Osaka station.
From Kyoto you can change the trains wisely and get to Kuwana with the train fare of 1,890 yen about one third of that if you use Shinkansen Bullet train to Nagoya and take Kansai train. It takes about three hours by local train so budget saving trip needs time and you will have to leave Kyoto early in the morning so that you can have both Jazzdream Nagashima and downtown tours.
From Kyoto take Tokaido local train and change trains at Kusatsu and take Kusatsu line. Then at Tsuge station change trains to Kansai line and at Kameyama change trains again for the train bound for Nagoya.
Vast majority of people come to Kuwana by way of Nagoya. From Nagoya there are two train lines that lead to Kuwana: JR Kansai Line and Kintetsu Nagoya Line. If you use Shinkasen or from JR local train line area such as Hamamatsu, or Hikone for instance, use Kansai line which usually depart from #12 or #13 platform. Nagoya people however, prefer Kintetsu line because Express trains stop at Kuwana. But for ordinary tourists finidng Kintetsu line is not easy because you have to walk about five to ten minutes even when you are aware of the entire map of Nagoya station area. Many of the Kansai line stations are unmanned but Kuwana is one of the popular places along the line and is definitely manned.
There is a bus service from Nagashima Onsen/Jazz Dream Nagashima to Kuwana, historical town known as the 42nd lodging station of Tokaido Highway from Edo(Tokyo) to Kyoto. It takes about 20 minutes by bus and bus fare is 500 yen for adult. You can buy a ticket through a ticket machine at the bus terminal near the Jazzdream Nagashima gate of Nagashima Onsen Resort Complex.
Shichirino Watashi or 28-kilometer ferry to Kuwana is no longer in service. So after visiting Atsuta Shrine get to Atsuta station and go for Nagoya station. Then change trains to Kintetsu line bound for Osaka and get off at Kuwana station. Kuwana castle ruins(Kyuka Park) and other historical buildings are about 10 to 15 minutes walk from Kuwana station.
There is a bus service for Mitsui Outlet Park Jazz Dream Nagashima from Kintetsu Kuwana station. Take the bus bound for Nagashima Onsen. Bus fare is 500 yen for adult. Adjacent to the outlet mall is Nagashima Spa Resort.