Here are some places I have visited in the past to enjoy Cherry Blossoms.
Hope you can have some time to enjoy this beautiful flower during your stay.
Shinjuku Gyoen ( Park ) . Yoyogi Koen ( Park ). Back Yard of Meiji Shrine ( from Sangubashi station of Odakyu line, it is 3 min. ) . Koganei Koen ( Musashi Koganai City ..... Take Chuo Line to west and get off at Musashi Koganei ). Inokashira Koen ( Park . Take Chuo Line to west and get off at Kichijoji station. Or Take Keio- Inokashira Line and get off at Inokashira Koen - Park).
Kinuta Koen ( Park. I forgot the nearest station, but it is in Setagaya-Ku. ) Chidorigafuchi. ( I think it is near British Embassy.)