If you're searching for traditional, or even untraditional, souvenirs in Shanghai, hop on over to Yu Yuan ("yuan" means "garden" in Mandarin). Here, you'll find a plentiful amount of tourists, locals scootering along on those silly wheeled sneakers shouting "Miss" or "Sir" asking you to buy bags and watches and a beautiful garden and architecture amongst it all.
Yu Yuan is one of the "must sees" of Shanghai. No matter which corner you decide to round, you will find a shop selling something you've told yourself you'll never need, but end up buying it anyway. Locals here are friendly and speak English rather well.
Put shopping aside and make sure to take in all the traditional architecture around. There are also many famous eating establishments inside Yu Yuan that serve dumplings and sweets.
Tip: 1. Haggling with the shop keepers at Yu Yuan is a must. Tip 2: Don't let them rip you off on knock-offs: be assertive or walk away to the next guy. Tip 3: Your two new best phrases are "Tai gui le" (thai-gway-luh) which means "It's too expensive" and "piyani" (pee-yan-ee), which means "cheaper." Tip 4: Keep in mind that the same thing you're looking at may be at a different shop in Yu Yuan, or even at a different tourist spot. If the price is not to your liking, simply walk away and watch the magic enfold. Tip 5: "Wo bu yao" - "I do not want" will come in handy more than you know.