Yang's is a Shanghai chain serving shengjianbao, a fried soup dumpling - crispy on the bottom and soft on the top, just incredible. Went here after visiting the World Financial Center, but there are many locations around the city.
The oldest halal restaurant in Shanghai, dating to 1891. They're known for mutton hotpot. Note: there are 2 locations, a shiny new one in People's Square, and the original (with gorgeous old entryway), several blocks south at Yan'an Lu.