How do you get from Hiroshima to Nagasaki?

Hi there,

Traveling from Hiroshima to Nagasaki --> Take the Shinkansen to Hakata (Fukuoka) and a limited express train from there to Nagasaki. The route takes around 190-215minutes depending on trains taken. Here is the Route in Hyperdia.

Traveling from Nagasaki to Hakone (or on to Tokyo) --> Take the train back to Hakata, you can get back on the Shinkansen from here. You will most likely have a transfer at Shin Osaka from one Shinkansen train to an other heading to Tokyo. You can stop along the way at Odawara if you wish to visit Hakone. Hakone basically is the gateway to Hakone and you can either take a local train or bus from here further into the region.
Here is the route in Hyperdia.

Have a good trip!
Daniel