Osaka is also worth a visit. There are some really good food places in Osaka, at Dotonbori. Osaka and Kyoto are 20 minutes apart via shinkansen (which is included in the JR train pass) or about an hour by normal JR trains. If you are going to Osaka, you can get an unlimited pass. The website contains info on what it covers and how to buy them
https://www.osaka-info.jp/osp/en/index.html
3000yen for a 2 day pass is well worth it, you will save so much money. I planned a route ahead so I was able to get 15 of the 28 attractions done. But I think I was a bit insane
Kyoto has the Lecia shop which is worth visiting. In Tokyo (or Osaka has one as well but I prefer the Tokyo one) go to Yodobashi in Akihabara.
In Tokyo if you want something different and a bit off the tourist trail, there is the Setagaya line which is a street car/light rail train thing. You can buy a day pass for it, which is quite cheap.. I believe they were 300yen last time I went on it. You can get off at each stop and visit the temples and shrines along them. One of the shrines is supposed to be where the Lucky Cat originated from.
https://en.wikipedia.org/wiki/Tōkyū_Setagaya_Line
Just remember that October can have typhoons so pack a rain coat, I wouldn't bother with a brolly. You can just grab a 100yen brolly from a 7/11 or another convenience store and continue on.. I was there during Typhoon Whipa. Going up the Umeda Sky Tower during a Typhoon was fun. They closed off the open top area shortly after I went up.
I also agree Golden Pavillion over Silver. But Kyoto has a lot of temples which can be interesting to go in.
If you want to do Onsens, I recommend going up to Hokkaido to Lake Toya. It is an Onsen resort town and I believe it is the most popular. You can visit any Onsen in the town, and there is a fireworks show on the lake. You can also go up an active volcano, Mount Uzu and see Showa-Shinsan which is a mountain which popped up in the 1940s. There is also some of the ruins from the last volcanic eruption which you can see, they have a public trial through it which is free to access. Hokkaido itself is also awesome for Landscape photography and well worth a visit if you are into that. If not, then stick to the cities.