With about two weeks remaining in March, it now appears all weather agencies are in agreement with the timing of the cherry blossoms in Tokyo:
As per the latest observations, the opening of the season is projected around March 23rd, with the full bloom coming on April 2nd. April 1st-8th is estimated to be the best timing in Tokyo for the cherry blossom viewing.
Will your visit be outside of this slim window? You can head to Shinjuku Gyoen National Gardens where there are 65 different types of cherry trees with some blooming through late April. The gardens will be open everyday during April from 9am to 4:30pm. (Note on the 15th, it will open from only 10:30am due to a ceremony hosted by the Prime Minister)