help finding a Sydney suburb

I am moving from Melbourne to Sydney due to my husband getting work in the city, I was hoping someone might be able to help me navigate where to live, I have family there but they love the city and I'm not interested in living in a tiny box apartment. So if anyone could help me find something close to what I'm after that would be great. I need a house with a yard as I have a baby and pets, I am looking for somewhere I can get to the shops with little effort as I have to take a kid with me every time I go, I also want somewhere I can walk my dog off lead. I would love a tree lined street but probably asking too much considering we need to have easy access to the Sydney airport. Any suggestions? Oh also I would prefer not to have to sell my organs to be able to afford it.