The Lord Nelson and Red Oak are definitely worth going to.
The Lord Nelson is a great old pub and has some nice British-inspired beers. The Hero of Waterloo, also in the Rocks, is a classic old pub but has gone a bit bogan - according to locals. The Red Oak has the best selection of different types of beers on tap than anywhere else in Sydney - as far as I know. There is a great 'speakeasy' type place across the street from the Red Oak called the Baxter. It's down a wee alley and in the basement of a building. Great whiskey selection. Very manly place with pictures of boxers and horse racing on the walls.
The Wig and Pen in Canberra is certainly worth checking out. Canberra is a bit of a dull place, but the Wig and Pen is just like a British pub with a great selection of locally-brewed craft beers. Check out the Australian War Memorial while you're in the 'bush capital' too.
My dad is from a town called Wagga Wagga, which is a few hours along the Hume Highway from Golbourn. There is a brew pub called the Thirsty Crow that is certainly worth a stop. Really nice pale ales with Australian hops. You'll find a really good American pale ale there too.
If you want to experience a slice of Australian pub culture, go to one of the megapubs in Sydney's western suburbs (the Ettamoogah, The Mad Fiddler or The Castle Hill Tavern). Huge pubs with violent reputations and not much craft selection. When in doubt, drink Toohey's Old.