You will make a long chain of trips on Day 3, so if your Osaka hotel is OK, you had better keep your extra luggage in the hotel.
What if I go to Arashiyama early in the morning? From Ryoanji to Kinkakuji, i prefer to take a bus. Arashiyama Station of Hankyu is located to the south of Katsura River.
Arashiyama Station and Randen Saga Station of Keifuku (Randen) are located to the north of Katsura River.
Torokko Saga Station of Sagano Scenic Railway is located near Randen Saga Station of Keifuku (Randen).
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http://www.japan-guide.com/e/e3912.htmlIt is about 5 minutes on a bus to get from a bus stop close to Kitano-Hakubaicho Station of Keifuku (Randen) to Kinkakuji-michi bus stop.
(On a map showing routes of Kyoto City bus and subway, I cannot find a bus stop located close to Ryoanji Station).
From Kinkakuji, how can I get back to Osaka namba? From Kinkakuji-michi bus stop it is about 14 minutes on a bus to get to Nishi-Oji Shijo bus stop. The bus runs southbound on Nishi-Oji-dori, approaching to east-west Shijo-dori.
You will get off the bus and walk to Shijo-dori and find an entrance of Saiin Station of Hankyu. (Keifuku also has Saiin Station, which is located a bit apart.) You will need to go down via staircases to the platform for Track 2.
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http://rail.hankyu.co.jp/station/pdf/map/saiin.pdfYou can change trains at the same platform in Katsura to a faster train for Umeda. You will make transfers twice more, at the same platform in Katsura in Awaji and changing platforms in Nippombashi.
One possible route on Day 3 is
from your Kyoto hotel to Karasuma Station on foot,
from Karasuma via Katsura to Arashiyama by Hankyu,
via Togetsukyo Bridge over Katsura River to Torokko Saga Station on foot,
from Torokko Saga to Torokko Hozukyo by Sagano Scenic Railway,
around the station on foot,
from Torokko Hozukyo to Torokko Saga by Sagano Scenic Railway,
to Randen Saga Station on foot,
from Randen Saga via Katabiranotsuji to Kitano-Hakubaicho by Randen (Keifuku),
from Kitano-Hakubaicho (bus stop pole located to the north of the station, on the west side of Nishi-Oji-dori)
to Kinkakuji-michi on Bus Line No. 205 (clockwise),
in and around Kinkakuji on foot,
from Kinkakuji-michi (another bus stop pole used by Line No. 205)
to Nishi-Oji Shijo on Bus Line No. 205 (counterclockwise),
to Saiin Station of Hankyu on foot,
from Saiin via Katsura and Awaji to Nipponbashi by Hankyu and subway Sakaisuji Line,
to Namba by subway Sennichimae Line,
to your Osaka hotel on foot.
Good luck!