As Coffee says, far too many to choose from. You'll never go hungry in Shanghai.
Of course, there's a lot of so-so stuff out there and, since we all have different tastes, you need to define "yummy".
In terms of areas of town.. again depends on taste and budget
Xu Jia Hui has a lot, Zhonghan Park has quite a few, the area around Shanghai Centre ( Nanjing Lu near Tong Ren Lu, has a quite a few, JingAn temple area has more than you want to visit. Xintiandi has a range of tastes. That should get you started. Let me know when you finish eating at all the restaurants in all those places. You should be able to write a book.