Tokyo will probably feel as dystopian as New York. The main areas are extremely densely populated, there are lights, videos, musics and noises everywhere, always hundreds of things happening around you. It's impressive. It's personally what I enjoy but I get why it's not for everyone. But by definition, it's a unique experience and the tourists are completely outnumbered so it feels really local. I was actually surprised each time I saw a tourist in the street. There are also some big parks in Tokyo for when you want to take a break from all the craziness.
About destinations where life goes a bit slower, it's hard to not recommend the classic ones, especially if it's your first time in Japan. 2 days in Kyoto, 2 days in Osaka, 1 day trip in Nara, 1 day trip in Kamakura, 1 night in a onsen… This is the traditional Japan. Since those cities are smaller and all the attractions are listed on every traveling books/sites, you will definitely see a lot of tourists, but you can't go to Japan and not visit those places at least once!
About destinations where life goes a bit slower, it's hard to not recommend the classic ones, especially if it's your first time in Japan. 2 days in Kyoto, 2 days in Osaka, 1 day trip in Nara, 1 day trip in Kamakura, 1 night in a onsen… This is the traditional Japan. Since those cities are smaller and all the attractions are listed on every traveling books/sites, you will definitely see a lot of tourists, but you can't go to Japan and not visit those places at least once!