We arrive in Tokyo April 22. We go to Kyoto April 24, Onomichi (to bike the Shimanami Kaido) April 27, back to Tokyo April 27. I’m assuming it makes sense to get the JR Pass? Also, when I search train timetables to get from Kyoto to Onomichi, it doesn’t look clear to me that I actually arrive in Onomichi? Thank you for any advice! We are very much looking forward to our trip!
As for doing the whole cycle run plus the way back to Tokyo in one day, it is doable but would be a rather long day. The cycling is 70 km and will take about 5 hours, plus there is the question of if you want to cycle back or take a bus back. If the former then you'd need a very early morning start and it would be very tough if not impossible in a day (the train ride alone would be close to 5 hours). If you take the bus back, the bus takes 90 minutes which makes it possible, but still a very busy day.
I suggest if you really want to do this, that you at least stay in Onomichi the night before your ride.
There is a lot of detailed info you should read on the cycling at:
I also highly recommend seeing the Kosanji Temple along the way, on Ikuchijima Is. It is so wildly ornate that many call it a "Buddhist Disneyland".