What cities to visit?

Hi everyone, I just want to know what cities should i settle down and from there commute via Jr rail. For example I should stay in Kyoto and from there commute to Nara and Osaka. Should I also stay i Tokyo and commute from Tokyo and other cities. How about Hiroshima or should I simply stay in Kyoto and travel from there. I plan to travel on December is this a good time to travel or not.

Yes, basing yourself in Tokyo and Kyoto and make daytrips into the surrounding tourist spots sounds like a good, often chosen way of travel.

For Hiroshima, it can be visited in a daytrip if you like to travel at a fast pace. However, if you prefer a slow pace, I recommend to overnight in Hiroshima at least once.

I plan to travel on December is this a good time to travel or not.

Tokyo and Kyoto are pleasant in December. In early December, you might still be able to see autumn leaves. In the countryside and mountains, however, most of the vegetation has become barren, and in higher elevations and northern latitudes, it has started to snow. So, except for winter sports, it is not the ideal time of the year for outdoor activities (hiking, landscape viewing) in the countryside. Not ideal does not mean that it cannot still be enjoyable.

are perfect for doing daytrips, thanks to the Shinkansen you can go very fast from one place to another. as said, Hiroshima and Miyajima can be done on a daytrip from Kyoto (but it gonna be a long day). From Tokyo you can go to places like Nikko, Kamakura, Yokohama, Nagano,Matsumoto etc etc. from Kyoto you can go to places like Nara, Uji, Osaka, Himeji, even Kanazawa, mt Koya and Takeyama is possible on a daytrip, as long as you plan these trips very well and don't bother for long days, and to spend a lot of time on trains (ie Kyoto to Hiroshima and vv, takes all together about 7 hours, take the first Shinkansen from Kyoto (around 6:00AM, arrive at Hiroshima around 9:30am, visit the A-Bomb dome, peace museum and go to Miyajima around 13:00, visit the temples and see the Torii, and go around 17:00 back to Kyoto, arrive at Kyoto around 20:30)