Sakura season (late March – mid April) is Tokyo's busiest. Hotel prices double or triple. Book 6+ months ahead.
Hanami (cherry blossom viewing) parks include Ueno, Shinjuku Gyoen, Yoyogi, and the Meguro River. Go early morning or evening for fewer crowds.
Golden Week (April 29 – May 5) is the second crunch period. Avoid it if you can.