I always shop at LUMINE shopping center. It's located in multiple areas such as Shinjuku, Ginza, and Ikebukuro. Some people like to shop at outlet malls, too.
If you are younger, like teenager, Shibuya and Harajuku would be suitable places for shopping. Go to Laforet Harajuku or Takeshita Street in Harajuku, or 109 shopping center in Shibuya.