I might be slightly biased but you can't beat Sydney. Love it love it love it! From the beaches so close to the city to the Opera House and theaters if you're feeling slightly more cultural. There is nothing better than the walk from Spit Bridge on the North Shore ending in Manly. It follows the coast and by the time you get to Manly at the other end, it is an excellent excuse for a chilled glass of white or a splash in the ocean. Cycling in the Blue Mountains (mind you that is probably a bit hard core depending on the ages of your children!) or kayaking around Middle Harbour, or just a day on one of the gorgeous beaches all in a stone's throw. The restaurant's are 'mostly' child friendly and the food is really fresh - my fave ever is Sails at the end of McMahons Point with a view of the bridge and Opera House. Having said that, as an expat I can't praise Australia enough and enjoy every minute here. So I'm sure there will be others who equally praise Melbourne and I'm sure for good reason. Wherever you settle, I'm sure you'll enjoy it, just be aware that it isn't all perfect and idyllic but if you are willing to give it a fair go, you'll benefit from all it can offer you. I 'm new here so I don't know if this is OK to do but I wrote this about my expat life here - hope it's ok to link to it? http://writerbeth.hubpages.com/hub/My-ex-pat-experience-in-Australia
Anyway, enjoy your holiday there to suss it out - it would probably pay you to try both Melbourne and somewhere in NSW like Sydney if you could manage it for a comparison. The more you see, the easier it wil be to make a decision, Thanks for listening to my slightly biased rant, Beth