Spring trip suggestions

Hello everyone
I'm planning my first trip to Japan, between 28.Mar.2017 and 14.Apr.2017. I'm a 34 year old man, will be traveling alone so I can go wherever seems interesting.
I've got a rough outline of my trip, and have already booked my accomodations as follows:
6 days in Tokyo, sidetrips to Nikko and possibly the snow monkeys, if they're still around in April
2 days in Hakone at a ryokan
6 days in Kyoto, sidetrips to Nara and Osaka
1 day in Hiroshima
1 day cycling the Shinamami Kaido bike trail, sleeping in Imabari
1 more day in Tokyo then homeward bound.
I will have a JR Pass for most of the duration, and would welcome any advice regarding additional places you think I should visit. I'm not very interested in stuff such as Disney / Universal, but more into nature, history and culture.
I've been lurking around these forums for a few weeks now, but any suggestions will be highly appreciated.
Thanks for the help.

The snow monkeys are there year-round, but they're more likely to go in the water in the cooler months. The keepers sometimes tempt them into the water by throwing food in, if the monkeys won't go in themselves. It's also more picturesque in winter, with all the snow around.

I'd extend your stay in Hiroshima by one more day so you can also visit Miyajima. It's a gorgeous place, and if you have a full day there you can do one of the hikes to the top of Mt. Misen.

You'll be in Japan during cherry blossom season, so you'll want to have all your bookings sorted ASAP. While in Kyoto, if the weather's good and the blossoms are in full bloom, consider a day trip to Yoshino - it's said to be the best place in Japan to see the blossoms. It does get busy though, so leave early - I left Kyoto at 6.30am and there were already lots of people there by the time I reached Yoshino. An hour later, around 11am, the main street was packed!

Thanks alot for your answer sq.
I've already booked everything so will probably miss Miyajima, however I intend to add Yoshino to the list of places to go to as it sounds great.