Which suburbs to visit in Sydney?

I'm going to be in Sydney next week - while there, i wanted to check out some spots that aren't your typical touristy spots - maybe see how the locals live, where they hang out. Where would i want to go in Sydney to see these spots?

Glebe and Newtown for the student area with an awesome bohemian vibe (especially Glebe Point Road). Or if you really want to see a more suburban area, just take a train out west to somewhere like Croydon (don't think you'd find much of interest there, though; I only ended up over there for a party with some local friends), or maybe even further to the Parramatta region (might be worth for then taking a ferry from there back to the CBD, allowing you to see the entire length of the harbour).

Sander is right, taking a ferry out to Parramatta and catching the train back is a good idea, and depending on the weather you could head either north to Narrabeen or south to Bronte to check out the beaches. Glebe and Newtown are pretty trendy, depending on your age you could always go to one of the Unis and hang out with some students for local ideas.

If you're looking for the more local beach experience
heading up north to avalon or palm beach is good, im pretty sure you can get a train and a bus up there
to be honest, theres not really much to experience out west, its a hell of a trek and not really worth it. as said before, Newtown, Glebe, Annandale, basically the inner west suburbs are probably your best shot. try a walk down king street in newtown for a range of cafes and more local pubs etc

hope it helps
enjoy your trip!

Some great pubs and nightlife in inner (inner-west) suburbs around Balmain etc.