We love the City Circle Tram! It's a great way to see the city for free. It can be difficult to get on and off with a pram but someone has always offered to help when we've hopped on.
You can hop on and hop off around the following Melbourne attractions:
Melbourne Aquarium
Federation Square
Flinders Street Station
Melbourne Museum
State Library of Victoria
Harbour Town
Docklands
Carlton Gardens
Here is a link that contains the timetable and a great map!