On Sydney. It has been suggested already to head to the Blue Mountains. I have always stayed in the Blue Mountains rather than Sydney itself (not a fan of big crowded cities). Trains will take you up there from the city. Katoomba is the number one destination and for good reason. I have usually stayed out a bit in cabins at the Blackheath Hol.Park. Bit quieter than Katoomba. Equally spectacular if you wander down to the Govetts Leap area. If you enjoy nature and stunning scenery the Blue Mountains have it in spades.
I am a Victorian.
Victoria is a smaller state than most but is very diverse. We have A grade coastal scenery, beaches, rainforest and many other forests, great alpine country and sub alpine country, lakes, rivers, deserts, farmlands and wineries. A huge capital city (Melbourne) lots of great historic towns. Pretty much got the lot and it is more accessible than in any of the other states.
You can get to or close to most of the top sights using public transport.
Not sure what your really looking for so I will just give you some of my faves and you can look them up if you are interested.
Heading up my way by train from Melbourne you pass through Macedon at the foot of Mt Macedon. Beautiful forests and gardens. Then Castlemaine, historic gold town, not far from another beautiful historic town Maldon.
Then my regions big smoke Bendigo. Impressive architecture as this was a big gold mining town in the mid 19th C.
From Bendigo PT will take you north to the historic river port town of Echuca. Take a paddle steamer ride.
If you fancy a desert type experience you could head further NW up toward Mildura.
West from Melbourne you will reach another historic gold mining town Ballarat, now like Bendigo a large regional city.
Further on you can reach Halls Gap at the foot of the Grampians mountain range. Might be busy in January. A bit further out is Dunkeld. Usually quieter but in an equally beautiful setting below the Grampians.
S.West through Geelong you can pick up the Great Ocean Road. This winds through magnificent rainforest and stunning coastal scenery through to the city of Warrnambool. You like museums? The Maritime museum at Warrnambool is worth a visit.
Keep Heading west you reach the impossibly gorgeous town of Port Fairy. Even further west is Portland, industrial (aluminium) but also beautiful and historic. Nearby Cape Bridgewater is a gem.
Continuing further west takes you across the border to South Australia. The town of Mt Gambier is full of caves, lakes, sinkholes and extinct volcanoes.
NE by PT you can reach the tourist magnet town of Bright at the foot of the Australian Alps. Across Tawonga Gap is the less tourist Mt Beauty.
From Bright you can access one of my favourite mountains Mt Buffalo. It is pretty spectacular.
You can also head out to lovely little Harrietville and access Mt Hotham one of our major skifields in winter. The Alps are quite stunning in summer (no snow though). You can hike from Harrietville up to Mt Feathertop (2d highest in Vic). I have over 40 visits so I do rate it. Not sure if that's your cup of tea though.
From Mt Beauty you can hike Vic peak number one Mt Bogong. Neither Feather or Bogong have vehicle access or any mechanical aids.
You can reach Phillip Island (SE of Melbourne) by PT with a bit of effort. Phillip Island is home to the famous Fairy Penguin Parade.
Further east is one of the jewels of Aussie National Parks in Wilson's Promontory NP. It is more of a challenge to access by PT however.
Closer to Melbourne. Healesville and the Yarra Valley are beautiful areas. Also the Mornington Peninsula and Western Port Bay. Summer school holidays though so expect big crowds.
Melbourne's lungs are the beautiful Dandenong Ranges, stunning forest not too far from the city.
I will post some further stuff on Melbourne itself and also Tasmania (if you are interested).