I'm not sure exactly what your definition of 'central Sydney' is, but the vast majority of the 'classic' pubs are in and around the Rocks area.
Personally my first choice would be the one you've mentioned - the Lord Nelson. It is a bit of a walk from the main area of The Rocks, but it's worth it. Not only is the pub itself impressive, but their on-site micro brewed beers are worth the trip alone! (Just be careful - some of them are strong!!)
On the way back (or to?) the Lord Nelson, there's the Hero of Waterloo (81 Lower Fort Street), which dates back close to 200 years and is definitely worth a visit.
Back over the other side of the bridge on Cumberland street there's the Australian Hotel. The pizzas here are great - get a half Crocodile, half Kangaroo if you want the real Australian experience :) On Cumberland is also the Glenmore - nothing overly special about the hotel itself, but if you can get onto the rooftop then the views alone make it worth the visit (the roof is often closed for parties/corporate functions/etc)
In the more mainstream area of The Rocks (ie, George St) you'll find no end of hotels, ranging from the Fortune of War (The oldest hotels in Sydney - worth a visit, but don't plan on staying long) through the Mercantile, and to the Lowenbrau (German - definitely not an Australian Classic!), and even Establishment if you've looking for something more modern (your father will probably want ear plugs though!). The Rocks area at night is beautiful, so you can't beat simply taking a stroll along George St and ducking into anywhere that takes your fancy!