We will need to choose only one of the cities for a 2 night stay. Which one is best
and why?

Melbourne is a much more interesting city than Canberra. Melbourne is quite cosmopolitan, with several ethnic neighborhoods, as well as a bustling downtown. The tram system can get you most places without a vehicle. In contrast, Canberra is rather sterile - the main reason to go there would be to look at the government. That is quite interesting, but on the whole, Melbourne will be a more vibrant city.

You don't say what your interests are, but unless you're particularly interested in studying Australia's history and culture, I'd suggest Melbourne.

ALF's opinion of Canberra, however, suggests either that he has never visited the city or, if he has, wasn't paying attention at the time. It's a cliched, stereotypical view that may have had some validity 30 years ago but has no support from the vast majority of visitors to Canberra and is hardly worth the effort of refuting.

By the way, if you're planning on doing any online research, the spelling is Canberra, not Cranberra (which if anything would no doubt return only recipes for cranberry sauce).

I have to agree that I wonder how long it's been since alf spent some time in Canberra. As an ex-Canberran, I know I'm biased but I really get annoyed with the constant canberra bashing that it is subjected to - not specifically this forum but in the media in general. Canberra IS a vibrant place, with a lot of variety to offer a tourist (both international and domestic). if you're into big bustling places, then sure, canberra won't hit the mark, but just because millions of people don't live there doesn't mean it doesnt have it's own merits. For example, if you like the outdoors, walking, cycling you can see so much of the city by these methods and there's plenty of bushland throughout the city with walking tracks (eg black mountain, mount ainslie behind the war memorial).

I went recently with sydney friends and they were all very impressed with the service in canberra as well, as opposed to sydney, which can be a bit snobby.

add to these things the national attractions such as the war memorial, national gallery of australia, parliament house (both old and new), the national museum of australia, which are all worth a look. plus you also have constantly growing wine scene within 20-30minutes drive ...

I'm not saying melbourne is not worth visiting, you can't deny that, but just that canberra is a worthy consideration for anyone visiting Australia.

Yes, lancefan has summed it up pretty well, and verareading, it has to be said that as it stands, your question is unanswerable - you need to give us some context, especially your overall itinerary in Australia and what you most enjoy doing and seeing; there's no outright "best". It's a bit like me asking which is the best city out of Boston and Washington DC. You may have your own views on that, but without knowing my interests I think you'd be hard pressed to answer such a question.

I would also strongly recommend that you don't rely just on the opinions of the posters here, either. If you'll be spending any reasonable amount of time in Australia a good guidebook is a must, supplemented by some research on the WWW.

ALF seems to be reflecting an old stereotype of Canberra dating from the days when it was a "company town". Nowadays significantly less than half the workforce is employed by government at any level, and the city is a de facto regional capital for south-eastern New South Wales, providing a diverse range of employment, education and health services for surrounding areas. It has a lively arts and music scene and excellent dining options in addition to its place as headquarters of the national government and many diplomatic missions and a growing high-tech sector. Like other Australian capitals it's also a very cosmopolitan city.