Melbourne offers great public transport services for tourists.  There is a bus that costs $10 for two days of hop on - hop off travel and a free tram service in the city centre.

The free Tram service  is  called City Circle Tram. They use older wooden tram cars for the most part, providing a special experience.  The route loops around the CBD, service goes in both directions. Stops are marked by a unique sign for the  City Circle Tram (different than the regular tram service). There is recorded commentary describing the nearby sites. The CBD is small enough that nothing is more than a few minutes walk from a tram stop. For more information: click here and map.

The bus route goes to areas outside the CBD. Service is every 15 minutes, and it's very easy to use, and has a really good map handout.    Look for the red & white coloured bus stops.  This link describes the route.  

Various maps and brochures, including the above routes can be downloaded from this page