Help please!

Hello there,

Kyoto → Fushimi Inari, travel to Inari station, about 6min from Kyoto station. (Direct connection from Kyoto station)
Kyoto → Arashiyama, travel to Saga-Arashiyama station, about 15minutes. (Direct connection from Kyoto station)
Kyoto → Nara, travel from Kyoto station is 60, 90min - direct connection.
Kyoto → Kinosaki See this route for example. About 145-160 minutes, depending on if you take a direct train or have a transfer at Fukuchiyama.
Kyoto → Hiroshima here is an example route.
Miyajima → Osaka See this route
Osaka → Tokyo, see this route for example.

Hope this helps,
Daniel