I don’t even know where to start foodwise… I also don’t know what your “tolerances” are with chinese food and what you already know anyway.
A must do in Shanghai is getting up early and getting a breakfast consisting of sheng jian bao and da bing (both typical street food). Also xiao long bao are a typical Shanghai thing but can vary widley in quality when bought at street restaurants (where it should be bought since it is not a “fancy food”, in my opinion). There is a ton of other street foods that is worth trying. Especially in Shanghai there is actually nothing sold on the streets that I would consider “uneatable” for western tastebuds - maybe chicken feet 
. Just try it all. Especially the semi-legal nightmarkets that suddendly pop up in the evening. Don’t mind all the scared westerners telling you the grim tales about gutter oil, I ate all that stuff for quite a while and I am just fine. Nothing of it will kill you, especially if you eat if for just a few days.
For restaurants the rule of thumb is: the more people the better, because you will usually share all the plates together. More people → more variaty of what you can order and try. And if you have some locals with you even better because they will know where to go and what to order. There are usually 10 decent restaurants on every street in Shanghai and they all do more or less the same stuff. Usually it is not worth it to travel over the whole city for some place to eat unless you are looking for something specific. If you don’t have locals to show you those places near you try couchsurfing. A lot of Chinese students are quite active there, eager to learn English and to show you their city. And most of them are foodies. Even if you are staying in a hotel couchsurfing is useful to connect. If you are alone and it is too “scary” to you to just walk into these really local looking restaurants and just order whatever (which is very understandable) you should try malls. In a lot of malls you have quite nice restaurants that strike a nice balance between quality and price and are usually very clean and have an “English” menu with nice big pictures. Personally I would stay away from the pricier, fancier restaurants. In my experience they usually just add spectacle, not necessarily food quality - something especially chinese tourists with a lot of money care about. Some of the best bites I actually had were in mall restaurants. You can even find quite experimental places there, you just need to know someone to show you since it usually is impossible to google it.
Any other specific things you are looking for? Maybe I can help. A bit hard to recommend if I don’t know what you are looking for… because there is plenty of stuff to do.