Melbourne city in 1 day ? It sounds like a tough plan considering so many amazing places to see and exciting things to do in the City.
Let me give you a hint about an itinerary which can help you in exploring the best places of city
Start the day by sipping a cup of coffee at Federation Square along with a sweet pastry (well that's just my choice). The view could be full of tourists or native residents running late for the work, but its worth to spend 30 minutes before you kick start the day.