While it's not really my thing and has been somewhat controversial due to legal issues, it's definitely a unique experience you can only find in Japan.

STREET KART Shubuya 1st is the most popular and reliable one based on review.

About:

STREET KART Shibuya 1st is a popular go-karting experience in Tokyo's vibrant Shibuya district. With its colorful costumes and themed tours, it offers a unique way to explore the city streets while channeling your inner Mario Kart character. From cruising past iconic landmarks to feeling the wind in your hair.