The Plaka is the hub of all the tourist shopping with souvenirs, clothing, and food at every turn. But you just can't avoid it, nor would you want to miss it. My fiance loved getting her hands on some wonderful Mediterranean fashions as we strolled up and down the tiny streets.
While it's a great stroll and quintessential experience, for better deals check out the areas just outside of the Plaka. Venture into the areas between the Plaka and Syntagma, and between Syntagma and Omonia. You'll find all the spots the locals shop, and at non-tourist prices.