Even in a lengthy city visit, if you tried to visit every restaurant once, you’ll never finish. You’d just feel burned out anyway.
A better option is to find a restaurant you like, and visit it several times. You’d be amazed how quick servers pick up on a familiar face. By visiting the same restaurant multiple times, you’ll begin to feel like a local yourself.
Repeat visits gives you a better opportunity to get to know the people who work there. Spend time learning about who they are, what their aspirations in life are, etc. As you do, you’ll get an increasingly better understanding of what growing up and living in that city is like.