Luna Park, in St Kilda, is a fun place to visit: very retro, a little shabby, loaded with fun rides. The highlight is the Scenic Railway, the oldest continuously-operating roller coaster in the world. Come on, you have to ride it! We're not talking thrills, we're talking history!
I live near Santa Cruz in California, and we have a pretty decent old wooden coaster, but this one at Luna Park is the real deal - it even has a chap in the middle of the cars operating a brake. Worth the trip to St Kilda on its own. While you're there, have a flake and chips and drink in the atmosphere of the place. Then back on the coaster. No chundering, mind.
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