Hokkaido Shrine Festival
If you'd like to enjoy an important festival with a local vibe, the Hokkaido Shrine Festival, held in Sapporo in June, is an excellent choice. You will get a real feeling of what a matsuri with Shinto roots feels like.
Central to the festival is the passing through the city of a procession of Shinto floats called "mikoshi'. People gather along the streets to view the passing of the floats. The event is a celebration of the arrival of summer in Hokkaido, the northern-most part of Japan. It is held annually from the 14th to the 16th of June. If you are in Hokkaido during that period, you're in luck! Not only will you be able to attend this festival, but you'll also be avoiding the rainy season called "tsuyu" occurring in the rest of Japan.
Musicians playing traditional instruments are part of the procession, and there are even some free concerts by local organizations such as this one performed by the police department!
What you'll see in abundance is people wearing summer kimonos called yukata. People dressing in these traditional bright garments contributes to half of the great atmosphere of this festival. Why not wear a yukata yourself? They can be purchased for about ¥7,000. They're very easy to find throughout Japan during the summer months.
A Japanese festival wouldn't be complete without the food stalls. You can try miso oden, which is a winter dish in most part of the country, but people of Sapporo have it in the summer as well. Also, there are plenty of grilled meat on skewers and some grilled cuttlefish as well that you should definitely try since Hokkaido is known for its delicious seafood.
If you happen to get to Sapporo just a little earlier, you can also attend the very interesting Yosakoi Soran Festival held from the 6th to the 10th of June (2018 edition).