It should be noted to take everything we all say with a grain of salt, each Sydneysider has soft spots for certain areas, and (generally) unreasonable / very reasonable hate for others! 
Living nearish to a train station is a very good point if you need to live further out from the city.
With the half an hour restriction, that rules out everything further west than Parramatta (Parra is probably 40 minutes but is a good cut-off point), All the Hills district is out (nice area, but expensive and probably the worst to get into the city from). Anything north of Chatswood is out and South of Mascot through to Canterbury.
Suburbs in that Goldilocks zone to avoid: I'll leave my personal bias out as best I can!
- Lakemba, Campsie (And areas in the Yagoona-Punchbowl area which is further out) as that is the current drive by shooting capital of the city. Not a true reflection on the suburbs but best to avoid.
- Mascot and the general Botany Bay area due to the airport.
- Glebe, Annandale and Camperdown. Great places to visit, good food but crazy priced for what you get.
And depending on your feelings towards Uni students you my want to avoid the Randwick area!
I'd suggest doing some real estate searches for the inner city and surrounds and see what areas strike you and then maybe ask us for the lowdown on them.
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