Some feedback:

1). Fuji Five Lakes area, while not far from Tokyo, takes longer than you think to get to by train. Once you get there, the area is best explored by car imho. Plus going from there to Kyoto by train is quite cumbersome, as I'm pretty certain the fastest way to Kyoto might be to backtrack all the way to Tokyo first.
2). Based on the above, I might suggest you spend the first two nights in Tokyo and then just do a bus tour on a day trip to Fuji Five Lakes. That would really simply the transport for you, lessen the # of times you have to check in/out of hotel, and then significantly shorten your trip to Kyoto on day 3.
3). Miyajima/Hiroshima is definitely doable as a day trip from Kyoto. Such day trip will likely involve leaving Kyoto before 8a, having ~3hr to see the Peace Park and have okonomiyaki in Hiroshima, 5+hrs in Miyajima, back in Kyoto probably ~9pm or so.
4). However, if you're also going to Naoshima (which I'm not familiar with), then it might make more sense to base yourself in Okayama for the portion of the trip where you're doing Naoshima and Miyajima. You could then consider checking out places like Kurashiki and Onomichi.