Probably the most famous dish from Shanghai is Xiao Long Bao. Known in the West by names such as "Soup Dumplings," "Pork Dumplings," and others, they are small, meat-filled dumplings with broth actually inside. One must either use a spoon to capture the wonderful broth or pop the whole thing in your mouth. Be aware: the second approach can scald your mouth rather badly, because the broth is hot. This is a must-order item at any Shanghai restaurant.
Eels are another Shanghai specialty. I generally like them in a simple stir fry with some scallions.
Shanghai-style chow mein differs from Cantonese chow mein primarily in that it uses much thicker noodles. Also, they do not pan fry their noodles, so they are soft and chewy instead of being a bit crunchy.
Shanghai cooking is not too heavy. It's not quite as light as Cantonese cooking. But they do tend to favor sweeter and thicker sauces.