What's the best city in Australia for a young student ?

It's hard to say without know where you are from exactly what is best for you. If you are from Canada or a Nordic country for example, where it is very cold, then I would suggest going more southerly (Sydney or lower), whereas if you are say California or Florida etc, Brisbane would be fine and if you are from the equatorial area, avoid more southern areas (like Tasmania) as they are too cold. Brisbane is rather warm (winters are lovely but the summers are hot and very humid). They have summer rain. Sydney is nice, but pricey. Melbourne is "temperate" on a world stage (neither super hot nor super cold), and is winter wet. Adelaide is similar. They have dry weather so their summers might reach 40 for short periods, but it's dry (whereas Brisbane's average is 30 degrees (and it can get up to 40) but 30 degrees in Brisbane is "hotter" or worse than Adelaide 40... Perth is pleasant. Beaches though, Brisbane and Sydney particularly are better at this (Perth, Adelaide and Melbourne are ok). Mountains, Brisbane, Sydney or Melbourne possibly the best. Most state capitals are pretty good for public transport, try and find something near a transport corrider (so near rail or busway / or a a corridor that has lots of buses...) Again, despite rumours that some places are "backwards" you'll find most places have culture / restaurants etc but you may need to talk to other Uni students. For example Brisbane is considered "backwards" but has a great music scene however you need to know what is good and what is not...

Adelaide. Minus the weather. Summer is very hot (40C), winter is quite cold (5C), and it can be a windy city.

Adelaide fits your description best. Uni SA is the best known for arts in Adelaide. It has everything you described and is the cheapest mainland capital city to live in. The climate is warm to hot and dry in summer, and cool to mild and a little wet in winter - a climate similar to that of parts of Spain or Greece. The Adelaide Fringe Festival is about to start, and is the best arts event in Australia IMO.

Hobart in tasmania fits your description, I lived in Hobart and you will fall in love with the city as soon as you hit the tarmak from the airoplane

its hard to find anywhere that meets all the listed criteria. I am from melbourne and would have obvious bias. the only concern regarding melbourne is that it is the coldest place on the mainland getting down to about 15 in winter. It has a very diverse culture and sport is a massive thing hear. Another option is sydney the weather is warmer and the beaches alot nicer. These 2 would be my preference. Another option is the gold coast which has nice weather beautful beaches and a party lifestyle with some good universities. I wouldn't recommend adelaide I think it is a little too slow going

There isn't a city in Australia that is not too hot, not too cold and dry at the same time. What you're describing would be Santa Monica in California. If we have a dry area, it's usually extremely hot! Some said Adelaide. That city gets very hot summers unfortunately but yet cool winters (not too cold, as you said), but it is most of the times dry. It's modern and a major city but alas it is too hot, although mostly dry. It isn't perfect for you, but it's the closest at least. Perth is also good as it's dry, but it's hot too. Do not try any city on the east coast because they're very wet, humid, hot and windy.