Just to add another NSW perspective - non-city.
It IS expensive. Rail travel is about the only thing I've found to be substantially cheaper - just under $12 return to the city (2h each way) - amazing! But you pay more than that to go 3 stops within the city to the airport - they really hammer tourists! Oh and car fuel is cheaper too - but cars themselves are more expensive. although they do last longer - when we moved out here 5y ago, we looked around for a car and I was horrified at the mileage (kilometreage doesn't sound right!) on them, but it's quite normal to get a car running for 200,000 km (about 125,000 m) and more here. Built differently, less damage, I don't know - but they seem to go for longer.
Food - the price of fresh produce varies massively week to week, which can make budgeting tricky! The supermarkets pass on all the price variations from the markets/supply and demand - sometimes this works in your favour, other times not so much.
Health - although currently bulkbilling makes GP visits free at point of visit, if the new budget is ever agreed, it will cost everyone to go every time. If you don't have a bulk-billing GP, it's $35 a visit round our way. Not sure what it's going to be if the budget gets full approval. You have to pay for children's prescriptions; you can take generics instead of named drugs and get them cheaper, but it's still around $18 for a course of liquid antibiotics. You don't get free anything for being pregnant either! We have health cover - you have 1 year from arriving in Australia to get private health cover without age loading. Australian citizens have up until their 31st birthday to get it without age loading as well; after that, they pay extra for every year over 31 they are. Being as how I was quite a lot older than 31 when we got here, I made sure we got it within the first year! Including ambulance cover. DS1 needed an ambulance a couple of years ago; the bill came to us and was, iirc, around $600 but our insurance paid it.
House prices where we are aren't in the astronomical bracket yet, thank goodness. But rentals can be! And are hotly contested.
Utilities - electricity is pretty damn expensive, but then it is in the UK now too, I believe. We have solar panels to offset the cost and have been very grateful for them - originally I calculated they would be paid off in about 8-10 years, but electricity prices went up so much that I reckon now 5-6 years is more like it.
School - non-city NSW, our primary school has a voluntary contribution of $20 per term. But DH is Australian, as are both DSs (one by descent, one born here) and so I am the only one here on a visa - if your children are on visas too then you may have to pay school fees for them.
We also have to pay for extracurriculars like gymnastics, as they bring in an outside teacher for it. But apart from that it's not too bad. As others have already said, children can start school between ages 4 2/3 and 6 - they must be in education by the time they are 6, but they cannot start unless they will turn 5 by the 31st July in the year they start. Most children who would be 5 in June or July hold back a year, so are nearer 6 when they start. It's easy to do here, and is in fact often recommended - they like the children to be socially and emotionally ready, as well as academically.
Things I miss most about the UK are central heating, a nice airing cupboard; being able to go out without being eaten alive by mozzies within 10 minutes; flat areas where I can walk and cycle far more easily than I can here (I know there are flat areas in Australia but not where I live, in the foothills of the Watagan mountains!); nice summer days (early spring here is the closest approximation). Small things, really. Big things I miss are friends and family of course; and my DSs growing up away from my Dad and sister and their cousins.