Tanabata (七夕) has origins in a Chinese festival of old and is celebrated not just in Japan, but in China and some Southeast Asian countries where it is sometimes referred to as the Star Festival. It is traditionally held on or around 7 July.
There are other Tanabata Festivals in Tokyo, but the Shitamachi Tanabata Matsuri held on the 1.2km stretch of straight road between Ueno and Asakusa is one of the most famous. Dancing, food and drink at local stalls, and traditional performances make for a great summer event among the warmer streets of Old Tokyo. Each day starts around midday and last into the evening. You can see the event schedule on the official website (Japanese only), but the parade is from around 1pm on the Saturday. The road is closed to traffic at the weekend.