we were in Japan in March and it was incredible! We visited Tokyo, Kyoto and Hakone and our tips can probably help you:
Exploring ＩＺＡＫＡＹＡＳＡＩＴＯ Izakayas in Tokyo is such fun! The price varies, from cheap to expensive, but at those cheap Izakayas under the railways, you would be able to experience real local Japan!
https://www.entaro.co has a number of interesting and reasonable experiences in the area. I took the sushi making course and had a great time
Hi Javier, Tokyo is very friendly with tourists and you will find people helping you even if not asked. On the other side, though, people don't speak English well but they do appreciate you trying speaking Japanese. Tokyo is full with things to see, including the famous temple of TokyoSensoji Temple, Ueno Parkand trekking on Mount Fuji . My suggestion is to experience traditions in Tokyo, such as tea ceremony, Japanese pottery, Ikebana or calligraphy class. I tried with Japanese pottery and I had a blast even if the teacher didn't speak Engilish, but it was very funny. You can try with this cultural organization: YANESEN CENTER. It is located in a tradizional neigbourhood of Tokyo and they have a Fecebook page. Have a good trip!
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You should try meet-up ! It's a great app to meet people, especially locals or people living there for a long time. Japanese people are not the most open people in general but some of them really like contact with westerners and will take part in things like meet-up or language practice cafés.
You can always try toursbylocal or something like that. Or couch surfing also does meetings.