Most hotels will sell day tram, train and bus passes ($7.00 for a day pass to get on and of as many trains, buses and trams, etc that you want).
There is also a free tram called the Circle Line - these trams are the original old wooden rattlers that used to get around the city in the good old days - that you can get on and off as often as you like for nothing. As the name suggests this tram does a loop of the central city of Melbourne past or not far from the main attractions - great way to experience a bit of the local history for nothing – stops include Flinders Station, the Melbourne Aquarium, across the river from the Crown Casino, the Docklands, the Parliament Building, etc.
Walking is also another alternative for central Melbourne as it is reasonably flat going and most sight seeing places of interest are within close proximity.
There are plenty of places where you can hire bicycles - as with the walking there are no steep hills and it is reasonably flat therefore cycling is a great alternative to walking.