It depends on what you are looking for.
If you are looking for clothes shopping, Shinjuku, Shibuya, Yurakucho/Ginza, Ikebukuro, and Harajuku (for younger generations) are the best places.
If you are looking for souvenir, Asakusa, Tokyo Sky Tree, Tokyo Station, would be one of the bests.
If you want to visit department stores, Shinjuku, Shibuya, Ginza, Ikebukuro are the places where multiple department stores gather.
If you want more tiny and nice commodities and souvenirs, Yanesen (Yanaka Ginza), Sugamo might be places.