Osaka-Kobe-Kyoto-Tokyo

Hi all,

Sorry for the lengthy post ahead! I was wondering if it is worth it to purchase a 7 days JR pass for my 1st solo trip to Japan (Dec 21st to Dec 31st)? I would also like to try taking the Shinkansen (Japanese Bullet Train) from Kyoto to Tokyo (Single trip) as an experience. If I going to purchase a 7 day JR pass when should i activate it to maximize my savings? Is it possible to do a day trip to Hiroshima as well from Osaka, what trains should i use then?

My itinerary is as follows :

Day 1 Touched down to Kansai Airport to Osaka
Day 2 Osaka (Day trip to Hiroshima if possible)
Day 3 Kobe
Day 4 Kyoto
Day 5 Kyoto
Day 6 Nara back to Kyoto
Day 7-10 Tokyo to Narita Airport