Two weeks based in Osaka and visiting the areas of the Kansai region is not unreasonable. For example, Himeji, Wakayama, Shima peninsula, in addition to Osaka, Kyoto, and Kobe.
https://www.japan-guide.com/list/e1105.html
You could easily add day or overnight trips from Osaka to Kinosaki, Okayama, Hiroshima/Miyajima.
https://www.japan-guide.com/list/e1106.html
Another thought would be to stay overnight in an onsen resort or ryokan, a wonderful experience, with many possibilities in the area. By staying in Osaka/Kansai you avoid losing time in transit to another part of Japan, checking out of/into hotels, etc.