I just got back from a whirlwind visit to Kyoto and Hiroshima. One of the most unique places I visited was Okunoshima, better known as Rabbit Island.
From Hiroshima, we took the Kare Line train to Tadanoumi Station it (took between 1.5-2 hours and about 2,700 Yen per person/round trip). At Tadanoumi, it was a short walk to the ferry (aprox. 300 Yen per person/round trip).
The island was previously used to produce chemical weapons. After World War II, the test rabbits were freed and eventually a resort was built on the island.
When you arrive on the island, a shuttle bus takes you to the hotel. There you can buy small cups of rabbit food for 100 Yen.
Rabbits are every where. Many will come up to you once they see you have food for them and will eat out of your hand. There were even baby bunnies.
My recommendation is to come late morning and to bring a picnic lunch. There are electric bicycles for rent, and multiple areas to explore on the island. I'm sure the rabbits that are farther away from the hotel will be grateful for the extra food. Heck, even bring some fresh veggies for them. They'd love it.