If you want culture, good restaurants and nightlife, go to Melbourne. I would never recommend the Gold Coast, its our (Australia's) poor excuse for Las Vagas. If you can't handle 5 degree mornings in winter time (now) Sydney and northern Australia is much better - closer to the equator.

There is always lots to do and see - if your into all the touristy things then all of the above suggestions are good.

Sydney is more expensive than Melbourne, and yes, shopping can be pricey. So is public transport (taxis, trains, trams).

Hope this helps.