michaelstuart wrote:Anything specific I should take on my first exploration? I am thinking water, food, camera, torch, phone.
Welcome to UEGA! The things you take on a trip depend on where you're going but I'd recommend at least gloves, torch and your phone. Your phone also acts as a good secondary torch if it has an LED flash. Water is a smart thing to bring regardless of location and even outside of urbex. A camera is not necessary, but many of us like to take photos to share the interesting bits and show off a bit. 
michaelstuart wrote:I am really nervous about getting busted by someone, could anyone explain the law in NSW to me regarding trespassing?
In terms of trespassing, if you get caught it'll be anything from getting kicked out to going to court. Going to court is usually reserved for high-risk locations or for disrespectful idiots. Don't do any live military sites or historical landmarks. Don't bring anything that could be used for graffiti otherwise they'll try to put "malicious damage" on you. In Australia, the safest form of exploration in terms of getting caught would be draining. However like everything we do, it can be dangerous if you're not careful. No drains when it rains!
michaelstuart wrote:Also what do you say to your parents? I am still a teenager so I'll probably say I'm taking photos (part true).
What to tell your parents? Sounds like you've got the idea already.
If you're nervous, get someone from the forum to go with you. As for locaions, Echo has already shown what most of us think when a newbie asks for locations without sharing anything.
I'm sure some of us would be happy to explore with you however and you will discover new locations from that.