Zhabei features some Shanghainese teahouses where you get either traditional or modernized dumplings and other small dishes to be had with tea or juice. And here the other customers are often born in Shanghai so both price and quality tend to be agreeable.

I'd also consider a day trip out to Suzhou for a Sunday lunch/brunch. Kempinski sunday brunch at Dushu lake, local fish and seafood at Taihu lake or elegant Suzhou classics at the more traditional hotels in the old town.