I suggest Daiso! We had the most fun shopping in that store! Very affordable and an enjoyable experience!!
I suggest to go to Laox. As I know there are 3 big Laox in Tokyo. 1. Akihabara, 2. Ginza, 3. Shinjuku. Ohh also in Odaiba. You can find everything in this shop as you want to buy many kind of snacks, cosmetics and electro devices etc... This is also duty free shop. So please compare the price w.other shops! Here is the web site. Enjoy your shopping in Tokyo!! http://www.laox.co.jp/en/stores/akihabara/
If you are looking for "the souvenir" kind of snacks, try hitting Tokyo Station. Along the main street from Chuo Line to Tohoku Shinkansen platform, there are several souvenir shops selling snack souvenir from Tokyo such as Tokyo Banana. Yaesu shopping street, also connected to Tokyo Station, is a good idea, too.
Tokyo Solamachi, connected to Tokyo Sky Tree has a good selections of snacks, too.
For cosmetics, drug stores like Matsumoto Kiyoshi or Donki is places you want to check. For high-end Japanese cosmetics, such as red lines of Shisendo, visit department stores.