While there are a ton of beautiful spots to partake in ?? - "hanami" or "flower watching" in Tokyo, I recommend spending a day of cherry blossom season in Ueno Park.
It's a huge park north of Akihabara, which means food vendors and performers can fill up the space in between sculptures and fountains. After you've gotten your fill of fried octopus - takoyaki - and cherry blossom-inspired ice cream, you can set up a picnic and eat and drink with the cherry blossoms overhead until the sun goes down.
Ueno Park is the perfect place for socializing, having a picnic, and experiencing the beauty of the cherry blossoms.