I wouldn't switch hotels to between Osaka and Kyoto as it is just 30mins by train between Osaka/Kyoto stations. Just stay in one or the other and take the train. Given the high number of tourists in Kyoto, you might find it to be cheaper to stay in a hotel in Osaka.

Just do 1 night in Hakone.

I'd recommend taking a day trip from Osaka/Kyoto to Himeji Castle. It is truly an amazing piece of architecture and one of most stunning buildings in Japan. Stop by Kobe on the way back and have dinner on the sea side.

EDIT: As the poster above said, Nara is great if you like history