Others have commented on the wisdom of how much you are trying to do, so I will just comment on certain parts. I have visited Tokyo twice on business trips where I only had one day on each for sightseeing. So, I have done two of the tours you are suggesting doing.

I have taken Sunrise Panoramic Tokyo tour and found it a useful way to see a lot of basic Tokyo sites in one day. Given the short amount of time you have, I think this is a good choice, even if you decide to spend more time in Tokyo.

I also took a one day bus trip to Nikko (I think it was from the same company). I found this to be a good break from the hustle-bustle of Tokyo and see some more natural surroundings. I enjoyed the temple itself, but it was the setting amidst the cedars and the landscape that really made Nikko special for me. While I know that you can go to Nikko on your own, I don't know if you can see the Toshogu shrine and Chuzenji-ko and Kegon-no-taki all in one day without the careful coordination and immediate transfers of a bus tour. Others will be able to advise you better on that score.

I have not yet been to Kyoto (I will be going soon and asking advice in a separate thread from the many much more experienced Japan visitors and inhabitants on this site).