If you're someone who loves quiet places, the National Gallery of Victoria offers free entrance. You can also access free Wi-Fi with a large area to be seated and spend your day on your own or with your friends.
If you're a music lover, plan a night at Cherry Bar on AC/DC Lane. You could get lucky enough to stumble upon free gigs and live music.
If you're a beach person, you can visit the famous beaches in Melbourne: Elwood, Brighton, Blackrock, St. Kilda, Chelsea and Port Melbourne. You have endless choices.