I took the XPT train to Broken Hill. It stops at Dubbo and you take a coach the rest of the way. Both are very comfortable means of travel and the scenery, although desolate at times, is fascinating (emus, kangaroos, sheep, rabbits, etc).
The normal price is $96 one way, but I paid $126 (30 to get there + 96 back to Sydney) because of a Mother's Day special! On the way back the path is slightly different and there are no stops to Sydney (approximately 13 1/2 hours to Central station).
I heard you can also get to Broken Hill by airplane (Rex airlines), sometimes for $125 only. Check their website!
I love trains. Going to Broken Hill it's the ideal way to combine a train ride with a good look at the scenery.
The Silver City Express (they use the term loosely) is one option or the Indian Pacific which goes all the way to Perth.
I caught one over and the other back last time I went.
This shot is from my second trip over and was taken about one month before they took this version of the Silver City Express off the line forever, though one of these has a home in the Hunter Valley (there were three) and is dragged out for historic trips for train buffs.
The Express ceased to exist for years but a local politician (for whom I am eternally grateful) horse-traded it back into being by offering his support for something else that was being voted on. It's now a longer train of different style.
The shed is also interesting. Trains have to stop at these widely spaced sheds as it is only a one line track and, by registering their presence, let other users know someone is on the line.
I'd recommend car over bus, train or plane, because once you reach Broken Hill, you're going to have to be able to get around to the various attractions, which are not all centrally located.