How many days are you here for, and do you want to get out of Sydney and see country/bush scenery? Car touring only, or does bushwalking interest you?
I'd be happy to take you out of Sydney. I'm retired, so have plenty of time.
Here's a 'Sydney in a one day bite' tour suggestion I wrote for a friend coming over from the States. He'd be starting off coming into the city by train from where he was staying in Hurstville. Ha ha, he's Chinese, people who know Hurstville will get the joke.
Of course this quick tour leaves out a lot.
Once in the city, get off at Museum station (underground), come up to surface at corner Liverpool and Elizabeth st. (Underwhelming 1st city view, deliberate.) Walk NE into park, to Anzac War memorial. Then follow centerline of park north.
Cross Park st. (Australian Museum is on cnr Park & College St, but that one takes all day)
Continue along center tree walk. Archibald Fountain in the park is one of the 'meet me at' icons in Sydney.
Just to the NE of the park, across Prince Albert Rd, is the Hyde Park Barracks Museum. Some buildings from the early days of Sydney settlement, with historical digs, etc.
Back at Archibald fountain head W, and down Market St, one block, to Centerpoint/Sydney Tower Eye, on corner Market & Pitt st.
Go up to the Sydney Tower Eye viewing platform. (they charge)
google maps 360 view from the tower here:
https://tinyurl.com/yaj6lo9uAfter seeing the view, you may have set yourself a list of city places to go. But if not...
At ground level, walk W on Market St to George st. You're then going to walk one block Sth to Town Hall station, but you can do it on George St, or through the center ground level of Queen Victoria Blg, or underground in Queen Victoria building. if you go underground it becomes a bit of a maze.
Come up to street level at Town Hall, for the buildings: the old town hall and St Andrews Cathedral.
Next go back underground into Town Hall station. (guess what it's underneath.)
Town Hall front steps on George St are another iconic 'meet me at' place in Sydney.
Take the train over the Harbor bridge to Milsons Point (1st station after the bridge.) (single, non-return ticket)
Use Burton St (I think) to go under the bridge train & roads to get to the East side of bridge, and the bridge pedestrian walkway.
(West side is cycleway, the East side is pedestrians.)
Walk south over the harbor bridge. Curse the bloody anti-suicide fencing. Especially since you are soon going to be at Nth Head, atop 200' cliffs with easily bypassed railings. (This is Sydney's preferred suicide spot.)
At Sth end walk through The Rocks area (kinda trendy) to the water's edge towards the ferry terminals.
Museum of Contemporary Art is on your right just before you get to the ferries. Takes hours to tour it.
Continue to main ferry terminal. Get a ferry to Manly. They all have some outdoors decks, for best view. The ferry route goes past the Opera House, giving the nice view from the water.
At Manly, you can walk East to Manly beach (another icon. Buy some chips or something and try to eat them on the beach, vs the world's most aggressive sea gulls.)
Get a taxi to North Head cliff lookout. (Walkable, but a waste of time.) Has a great view back across the harbor to the city.
Taxi back to the Manly ferry terminal, return to Circular Quay. (Don't be tempted to get a taxi all the way back to the city, it's a f*ckaround. Btw, Taronga Zoo is also best reached by ferry from Circular Quay.)
From the Circular Quay ferry terminal walk around the shore to the Opera House.
Then continue on Eastwards around the shore into the Royal Botanical Gardens. (A large area, if you want to see it all, get a map.)
If you leave the gardens via Art Gallery Rd (Eastern side) then you'll pass by the Art Gallery of NSW. More hours to see that.
Coming back via Art Gallery Rd you can walk to St James station (there are several entrances at the Nth of Hyde Park) or you can walk down to the Domain Car park entrance (building in middle of a field here:
https://www.google.com.au/maps/@-33.8707372,151.2153891,21z/data=!3m1!1e3) and take the longest moving underground walkway in Southern Hemisphere to St James station.
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The Powerhouse museum isn't in that path. You can walk to it from the CBD, or get the train to Central and walk from there. As always, the first thing to do in any new city is buy a street map. Sydney is nice in that it's small enough that a map of the central area fits on a single sheet. Also all train stations can provide a map of the rail system. There are no 'train tickets' as such any more, just an RF-tap based card system. Ask at stations.
I can also arrange 'urbex' type experiences too, if you're into that kind of thing.