Twice a year—when the cherry trees bloom and again in late autumn—Inui Street (乾通り) in the grounds of Tokyo Imperial Palace is opened to the public. The 1km walk starts from Sakashita Gate and ends at the Inui Gate on the north side of the palace (visitors also have the option of turning right and heading directly to the East Gardens).
As the street is within the grounds of the Imperial Palace security checks will be in place and you should be prepared for a bit of a wait to enter, especially at the weekend. Inui Street is open from 10am to 2:30pm each day. See the official website for detailed information in English.
See here for a run-down of places to see the cherry blossoms in Tokyo.