Every spring, staff from the Japan Meteorological Agency keep watch on one Somei Yoshino tree at Yasukuni Shrine, and when it shows five or six open flowers they declare Tokyo's cherry season open. That normally happens in the second half of March, and a lot of visitors book their trip around it. They shouldn't. Full bloom follows a week to ten days later, which is why so many holidays timed to the declaration end up under branches with a few brave flowers on them. If blossom is why you are coming to Tokyo in March, book the last ten days and stay into early April if you can. If it isn't, come in the first half, when the plum trees are out and nobody minds you ignoring them.
In March, most of the masks on the Yamanote line are not about colds. Cedar pollen season around Tokyo runs from about mid-February to the end of March, and millions of residents spend it quietly miserable. If you get hay fever at home, pack your antihistamines whichever half of the month you pick.
Ueno and Yoyogi are the party parks: blue tarps and beer, with ground staked out from the morning for the evening's drinking. Fun once. Meguro River is lovely and absurd after dark, so walk it on a weekday morning instead. For room to sit, head west. The Zenpukuji River green space in Suginami, a short walk from Minami-Asagaya station, has long runs of riverside cherries and far fewer selfie sticks, and Koganei Park, further out, has around 1,400 cherry trees of some 50 varieties.
March lows sit around 5°C, and evening hanami means hours sitting still on cold ground. Dress for winter. The cheap blue tarps sold in every convenience store keep the damp off, but the chill comes straight up through the plastic, so bring a folded blanket or a cushion to sit on.
If you have made the classic mistake and arrived for the declaration, go to Rikugien in Komagome. Its huge weeping cherry tends to flower about a week ahead of the Somei Yoshino and is lit in the evenings on a separate ticket. Later in the month, the Sumida River walk from Azumabashi to Sakurabashi is the classic. Watch for Vernal Equinox Day, a public holiday around 20 or 21 March, which turns any neighbouring weekend into a crush.
For a central park without the party, pick Shinjuku Gyoen. Alcohol is banned and bags are checked at the gates, and that is exactly why it feels civilised. On the peak weekends you need a timed booking, but in recent seasons the booking has covered only the middle of the day, so anyone at the gate for opening time can still walk in.