As of September 2009, Melbourne is my new home and the plan is for it to stay that way for a good few years. We've been pretty flat out getting the necessities sorted since our arrival here late September, so I haven't a lot to add as yet, but I'll put in a few pointers below.
Public transport is not the cheapest, but it's very convenient and AU$6.8 gets you an all day pass that covers more or less anywhere you want to go by train, tram or bus. The network is extensive and all forms of transport run frequently from early in the morning to late at night.
You'll never go hungry if you're anywhere near the CBD; there are more eateries here than anywhere else I've ever been. Chinatown has surged beyond its original borders and flooded the town - Chinese, Korean, Japanese, Vietnamese and Thai places can be found almost anywhere. If you're hungry, just keep going the direction you're going and you'll come to one soon enough.