All the Tokyo parks will have blossom in a prettier setting but they will be overcrowded for the peak of Hanami. Big temples and castles will also have pretty gardens with blossom. If you get there before cherry blossom, you can also see plum and peach blossom which is pretty too, but not as spectacular in volume. I don’t think there’s much natural about cherry blossom, it is a deliberate thing. For more nature, look for the popular mounts and mountains, some are very accessible by public transportation like Mount Takao or the various mounts in Hakone.