It looks you'll be traveling during New Year's in Japan. Word of caution, the days leading up to and right after Jan. 1 will be some of the busiest travel days in Japan. Its similar to our Thanksgiving holiday, where people go back to their hometowns.
One common piece of advice on this forum is picking a base for a couple of days in a specific area. For example, you listed Osaka and Kyoto. You could base yourself in Osaka and go out to Kyoto, Himeji, or Nara. These places are about a 1-2hrs away and make good day trip options.