Tokyo, Kyoto, Nikko, Nara, and Hiroshima are all visually such fascinating places that you could take a single prime lens and STILL have far more photo opportunities than you could possibly shoot in a whole lifetime!
I live up north, but when I went down to Tokyo last year, I took my 35mm and 85mm primes and a Tokina 19-35, and I was very happy with my selection of images when I got back. I kind of wish I had taken a fast 50mm prime as well and left the 85mm in my hotel room at night, as 50mm requires less shutter speed for static subjects than an 85mm.
You will likely be walking til your feet are blistered, riding public transportation packed tight as a sardine tin, and threading your way through masses of people bumping you with their elbows, so I would wear good walking shoes and try and keep the photo gear as light and compact as possible. I would not carry a tripod (I did that at a tourist spot up here a couple of weeks ago, and it was a disaster).
Basically, just take what lenses you normally enjoy using the most and don't mind carrying all day long.
Check the internet for festivals--there are always some going on--and make sure you attend at least a couple while you are here, as they are the best photo ops of all!
Julie