In McDonald's branding history, Melbourne opened the world's first McCafé in 1993.
The first McCafé opened at a McDonald's restaurant in Melbourne, Australia, in 1993. The concept added a café-style coffee counter and a more specialized coffee identity to the existing fast-food restaurant. Its branding helped McDonald's compete for customers seeking espresso drinks and café products.
McCafé later expanded internationally and became a distinct sub-brand within many McDonald's markets. Menus, store layouts, and launch dates have varied by country, so the global rollout did not happen everywhere at the same time.
Melbourne is the specific answer because it was the location of the first McCafé, not because it was the first city where every McDonald's restaurant served coffee. McDonald's restaurants had offered coffee before the McCafé concept; the innovation was the dedicated café-style format and branding.