Shopping in the Plaka
You can't not just avoid it. The Plaka is the hub of all the tourist shopping with souvenirs, clothing, and food at every turn. My fiance loved getting her hands on some wonderful Mediterranean fashions as we strolled up and down the tiny streets.
I will say though to also check out the areas just outside of the Plaka for even better deals. Venture into the areas between the Plaka and Syntagma, and between Syntagma and Omonia. You'll find all the spots the locals shop, and the non-tourist prices.