Greyhound use the Hume Fwy/Hwy shortest quickest but most boring route between Sydney and Melbourne and only two cities of any size, one Goulburn not having anything of any real note to stop for and then you have Albury on the border at the River Murray, and there's not a hell of a lot more to make it worth a stop.
Generally speaking, you need to get off the beaten track to find interesting places, a trek out to Bathurst for Mt. Panorama 1000Km race on this weekend would be one highlight, and drive around the circuit (a public road) when no race on of course is a great drive in itself, and then backtrack for getting across through Jenolan Caves to the Hume and then off to Canberra is another option before either continuing down through Alpine territory into northeast Victoria or back towards the coast and taking the coastal route.
If you're a driver, doing a campervan relocation -
Rental Relocations Australia New Zealand United States Canada - Hire Now at StandByCars is what I would recommend to see best of country between Sydney and Melbourne, going via the coast or at least to as far as Batemans Bay before heading inland to Canberra and then Cooma and the Apline Way into North East Vic. - have a look at
www.travelmate.com.au re guiding with detailed directions, and if driving yourself (even a few days car hire would be of value), and if heading south out of Sydney on the coastal route take a turn into the Royal National Park at Heathcote and do the Lawrence Hargreaves drive - spectacular.
If you're stuck with public transport, I'd look at your future travel and save the greyhound pass for that and get a ticket/pass with
www.premierms.com.au as they go via the coastal route and there are quite a few picturesque sea side villages worth stopping at, and some from where there are island and inland/national park tours available - Batemans Bay, Narooma, Merimbula, Eden, Lakes Entrance being main stops to consider and if driving, Mallacoota Inlet, Wilsons Promontary and Phillip Island could be added to the list, taking a cheap tent if not doing a relocation will pay for itself with free overnighting possibilities.