First up, I'd say Ginza might suit the more mature shopper, it's full of fancy department stores and boutiques, plus it's a pleasant area to walk around. North of Ginza is the Tokyo Station and Nihonbashi districts, both walking distance, and I'd recommend the Mistukoshi and Coredo department stores for some high-end and traditional Japanese shopping.
Next on the list would be Omotesando and Aoyama (we actually have an Omotesando walking tour itinerary here.) This area houses a lot of flagship stores for top fashion brands, as well as containing numerous architectural delights and oddities.
Daikanyama and Nakameguro are great spots for more contemporary, dare I say hipster shopping, we also have an itinerary for this here.
Finally the two busiest shopping districts are Shinjuku and Shibuya, though Shibuya is caters more to the <30 something age group both have a little bit of everything.