I live in Sydney and when we have guests come we split the city up into 2 day trips. One of these focuses on the area close to Darling Harbour the other near Sydney Harbour Bridge and Opera House.
My suggestion is for the second option, as you will be able to get a good glimpse of Darling Harbour from your hotel. The bridge and its surrounds are supposed to be Sydney's main attraction; it would be a shame to miss.
From your hotel (I am assuming is the Four Points Sheraton), walk up King St until you hit George Street. From there you should be able to get either a bus or taxi very easily. Ask to be taken to Circular Quay (most buses going on George St are going to Circular Quay).
From Circular Quay walk along the foreshore until you reach the Opera House. Here you will get plenty of opportunities to take nice photos of the bridge and also the Opera House.
You can go inside the main entrance of the Opera House and walk to the first level (a flight of steps) then walk outside some glass doors to your left you can get some good pics of the bridge from there.
Walk down the large steps surrounding the Opera House forecourt and head down and to your left towards the entrance to the Botanical Gardens.
When you walk in through the gates of the gardens, don't follow the waters edge (maybe you can take some photos along the shore then head back to the entrance). There is a path that goes up and to the right (it is more the middle as there is another path that goes up and does a sharp right turn and loops back on itself, don't follow this). If you are on the right path you will see this lovely big fig tree https://ssl.panoramio.com/photo/53022858 that everyone likes to take photos of.
Keep following the path until you come to a junction, you want to take the Macquarie St exit (see the little green sign in the center of this map which says Macquarie Street Exit).
From the exit it takes about 20 minutes to walk to St Mary's Cathedral (just keep following the road).
On the way to St Mary's Cathedral there are some places of interest that you may want to stop at, but don't make yourself too tired because you don't want to bomb out before you reach the Cathedral.
The Cathedral is very impressive and is open to the public (unless there is a state funeral; unlikely but this has ruined my visitor's plans once before). Inside the Cathedral photography is not allowed, but it still worth having a good look around.
Now once you have exited the cathedral it is time to assess how tired you really are. This is not a good place to buy food so I usually offer my visitors two options from here:
- Get some food and then do shopping / go home
- Sally forth and check out some of the other sites nearby
Cross the road to Hyde Park and get some photos of the Archibald Fountain. From the cathedral in a literal straight line from cathedral to fountain to other side of Hyde park you should end up and the beginning of Market St. Walk down Market street until you hit George St where there is plenty of food or just keep walking approx. 6 blocks and you will be at Sussex St where your hotel is (or get a taxi).
Near the entrance to the cathedral is the Fragrance Garden, a small patch of green if you are interested in that.
About 5 minutes walk; if you walk out the door of St Mary's and just keep walking straight, avoiding the fountain, and cross the road you will be at the Australian Museum. I've loved this museum since I was a kid, but not everyone loves museums, but there is one section where they have plenty of real, stuffed (dead), native animals which you could take some pictures of. They usually have some interesting stuff there.
Opposite either the church or the museum is Hyde Park. This has both the Anzac (war) Memorial and the Archibald Fountain. The fountain is definitely worth checking out.
I want more!!!
If you want to go home, go back and refer to the 'Heading Home' section above. If you still have a spring in your boots I suggest you walk to Centre Point Tower. It costs a few dollars to go in, but it is worth it for a glimpse of the city from above. You go up very high to the top of the tower and you can get a good 360 degree view of the city.
If you are still going strong, walk to George street (on the way back home) and check out the Queen Victoria building. This is an elegant building with lots of interesting (but expensive) shops.
From the QVB, walk to the North end of the QVB and you can then walk down Market street towards your hotel.
I suspect all of the above would take about 5 hours so you can decide on what you want to see or if how tired you are. I normally make this a full day when I have guests as we take a ferry in the morning from near my house and also include lunch. It is a very full day, but allows you to take in many sights.
I also suggest you take plenty of food with you as you can find yourself in certain parts of Sydney where there is not easy access to a range of food (near Hyde Park for instance). And you don't want to waste your time wandering in circles looking for a bite.
On Macquarie Street just after you pass Parliament House is Sydney Hospital. There is a small kiosk there where you can buy a meat pie or sausage roll. If you are hungry (and not a vegetarian) you could try a meat pie, this is real Aussie food, suggest getting some tomato sauce to go with the pie. Then you can tell friends you've tried some traditional Aussie food.
Also not far from the kiosk by the side of the road out the front of the hospital is a statue of this boar. Just something interesting to look at while you enjoy your pie.
Welcome to glorious Sydney, I hope you enjoy your stay!