At the center of neighborhood life since 1867, South Melbourne Market (southmelbournemarket.com.au) has an outsized reputation for its food, especially its international selections (the Dim Sims stall has operated here since 1949!). It's possible to book a 90-minute specialist Foodie Tour ($79), but there's plenty of enjoyment in simply wandering around and grazing as you go. Aside from Dim Sims' famous cricket-ball–sized dumplings, try the paella at Simply Spanish and freshly shucked oysters at one of the two oyster bars.
The market is only open on Wednesdays, Fridays, Saturdays and Sundays, from 8am. Keep an eye out for night markets in summer.
Two hours free parking is available on market days.