How to travel between Iga Ueno and Osaka
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http://www.japan-guide.com/e/e4353.html?aFROM=2157_4350At which station in Osaka will you board a train?
If I were in your shoes, I would visit Nara City in the morning and Iga City in the afternoon.
Logically you can use your rail pass on JR-West until Iga-Ueno Station.
However, the time to make a transfer will be less than three minutes, which may well be not enough for showing your rail pass and buying your Iga Tetsudo ticket around the transfer gate.
So, I suppose you had better not to stick to your rail pass; the one-way fare from Nara is only 650 yen. Maybe you can purchase in Nara Station a transfer ticket at 900 yen.
Note that trains are available only once per hour around noon from Nara via Iga-Ueno to Ueno-Shi.
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http://www.hyperdia.com/en/cgi/en/search.html?dep_node=NARA&arv_node=U...On the way back you can have enough time in Iga-Ueno Station.
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http://www.hyperdia.com/en/cgi/en/search.html?dep_node=UENOSHI&arv_nod...Todaiji Daibutsuden Hall is open from either 7:30 or 8:00 depending on seasons.
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http://www.japan-guide.com/e/e4100.html: You can catch a Line No. 2 bus from Pole No. 1 of the terminal in front of Nara Station. In about five minutes you will get to Daibutsuden-Kasugataisha-mae bus stop around an intersection near Nandaimon Gate.
: It may take about 10 to 20 minutes on foot from the bus stop to Daibutsuden Hall.
: Line No. 2 is a loop line. After visiting Todaiji you can catch a Line No. 2 bus from the same bus stop, but it will take about 15 to 20 minutes to Nara Station.
: Buses for Nara Station are also available from a nearby bus stop on Line No. 1, which is also a loop line.
: The bus fares (200 yen per ride) are not covered by your rail pass.
Iga-ryu Ninja Museum is open until 17:00, so you can get back to Osaka City by the midnight.
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http://iganinja.jp/en/museum/index.html