Tokyo > Kyoto > Osaka > Okunoshima > Tokyo

I'll be arriving with 3 other American's in Haneda Airport on September 3rd. I wanted to know what is the best option to get to Osaka from there? I booked the Gravinia hotel which I believe is attached to the Osaka station so I was just wondering what my best option from Airport to Hotel :). Secondly We will be spending the next morning attempting to arrive on Bunny Island, Okunoshima, can someone give me super detailed instructions on how to get there and maybe even back as Ill be spending day #2 in Osaka? From what I read Osaka to Kyoto is straightforward, and that will be my last day in central Japan before I head back to Tokyo which I believe is also just 1 Shinkansen. Any help is appreciated!