[Nyororin]

You could try Nagoya, which is actually the third major city after Osaka (Kyoto is very small in reality... only major as a tourist spot)
It sits pretty much between Tokyo and Osaka, so I have no doubt that you`ve traveled through it countless times. As a base, it would make a very nice place - Besides the city itself you have Gifu and all the stuff up there to the north, and Mie to the west.

I wish I could give advice on travelling alone, but I live here so any solo traveling experiences have been after reaching fluency... So I`m sure it`s quite different than your situation.