The Fayencerie in Vannes located in the medieval town, near the eglise has beautiful pottery for sale. Though not exactly local to Vannes-proper, the pottery is very popular with locals and tourists alike.
The boutiques of the medieval town are best for prime-time shopping: find clothing, nautical-themed gifts, lingerie, home and bath goods, jewelry, and many other gifts.
The larger stores like Carrefour and Leroy Merlin are off the main highway, all centralized. There are many good independent stores mixed into the mass development.