Dintaifung is a great Shanghainese and dim sum-like restaurant in Xintiandi. Ironically, it's a Taiwanese chain with locations across China and Asia (and one in LA), but some say Dintaifung has some of the best shaolongbao in the city (my favorite for now).
For the shaolongbao, they come in sets of 5 dumplings. I would recommend the standard pork, pork with hairy crab, and the chicken. All delicious and quite different. Drip out the sauce and then slurp the whole thing (and be careful not to burn your tongue if you decide not to let out some of the hot soup first).
I have brought vegetarians who were quite happy as well. Many veg/tofu dishes if you want and all quite good. Raw cucumbers with sesame oil and hot peppers. A bean curd and mushroom dish, quite some heat. Veg dumplings. Veg and pork and veg pork buns. Mushrooms with oyster sauce. Noodles with peanut sauce. Fried rice with egg and scallion. My favorite of the green dishes is the morning glory with ginger.
Located on second floor of the mall-like complex in Xintiandi.
2/F, South Block Plaza, Lane 123 Xingye Lu, near Madang Lu
新天地南里广场5楼, 兴业路123 弄， 近马当路
Phone: 6385 8378