<font face="Verdana, Arial, Helvetica, sans-serif" size="2">Originally posted by TonySCV:
The main criteria:
1. We want to stay somewhere nice, comfortable and quiet (for example, the Westin Sydney sounds fabulous, but I get the impression that the only people I'll be seeing in the lobby are folks over 50 (we're in our late 20's early 30's). The W Sydney sounds very cool, but the noise issues I've been reading about are a definite turnoff. For $200 a night I want quiet. 
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I am in your age group, and find the Westin in SYD and MEL to be reasonably high on the "coolness" side of things, generally a good mix of guests, and attentive staff.
In Melbourne make sure you get out to the urban "villages" centred around chapel street, lygon street and brunswick street - good food, good nightlife, and good shopping.
Canberra is a little more tricky - Starwood are yet to build me a local! So your options are probably as follows:
The Park Hyatt is very nice (and quiet) (and located within fairly easy walking distance of the major national attractions, ie Parliament House, the National Gallery of Australia, the National Museum etc), the other choices would be the Crowne Plaza (located in Civic - the retail/commercial centre of Canberra, so close to bars, nightclubs, shopping etc), or Rydges Lakeside (which is kind of between the two - on the outer edge of Civic).
Two days is probably about right if you want to see canberra, the Public Transport is quite good, and the attractions largely clustered around the lake.
Happy to provide anymore advice you need.
Matt