Xiao Yang Sheng Jian Guan is Shanghai's most famous location for shengjian or pan-fried dumplings. An order of dumplings runs RMB 4.5 and they're so delicious, you may want to order two, just be careful when you're chomping down on the shengjian, it is filled with delicious, but very hot juices. 

Xiao Yang's is so popular that there is a second location just next door at No. 45, but the No. 60 is the classic venue. If you have the time, wait for a fresh batch of dumplings, it'll be worth the trouble.