There seems to be only two main bike paths in all of Melbourne: along the Yarra Trail and around the Bay. Are there any others?
You might like to try Bikely: http://www.bikely.com/listpaths/country/14/region/1/city/1225 over 7 years ago
Greater Melbourne has around 2000km of cycleways. No other city in Australia comes close to possessing the cycling infrastructure of Melbourne. I don't have any particular recommendations, but needless to say there are cycleways everywhere, in most every suburb.
You can try http://www.melbournecyclist.com/ for starters. I'd suggest finding a good book (again, no particular recommendations - it's been a while since I lived in Melbourne, sorry) if you're going to be in Melbourne for a while and plan to do lots of cycling. over 7 years ago