There's a good thread going in Talk about the best food places for a tourist to visit in Manhattan. Commenters have named a few great places—classics like Katz's Deli for pastrami and Russ and Daughters for smoked fish, but also DiPalo's Fine Foods in Little Italy, Thai from Sripraphai, and massive candy store Economy Candy.
Tourist eats might not be the meals a local would eat every day; I don't know many New Yorkers who make a daily lunch of Katz's massive $15 sandwiches. But every town has a few places to show off.
Where would you take a tourist visiting your city?