Beautiful, but not too touristy: Negishi and Gumyoji
My two favorite spots near Tokyo are Negishi Park and Gumyoji. During the day, I go to Negishi Park, which is a huge park with innumerable cherry blossom trees. It is so fun to have a picnic with your friends and play badminton or catch during this beautiful season. The parks is a great place to relax!
At night, I always go to the river near Gumyoji station. The cherry blossoms at night are called "yozakura." They are so pretty at this park, because the cherry blossoms are lit up and the lanterns create a festival-like atmosphere. There are also "yatai" or stalls along the streets, where you can buy your dinner and snacks! My sister eats yakisoba (fried noodles) all the time. Although my family and I just walk from one end of the river to the other, you can also stay in one place of the river by sitting on a stool or using a picnic sheet.
Though not so touristy cherry-blossom areas, depending on the time and day, the parks can get crowded with locals! However, because it does not get extremely crowded, these are great places to relax!