Bro, I did almost exactly this a few months ago.
It was such a hassle. You have to lug your work gear everywhere with you. If you have Teams meetings, you will need wherever place you go to to be super quiet, and that rules out any cafes or restaurants because you have no control. A boisterous group of wanker customers might walk in right when you're talking in the meeting, for example. I didn't think you can use libraries because there YOU would need to be quiet, so how are you going to talk in the meetings?
One solution is to use one of these, but I don't know how long they will be around for, looks like the company is going to go bust:
https://www.taskpod.com/pods/list
The CBD one in the Picadilly building is pretty good location wise. Close to CBD Style and close enough to Surry Hills.
EDIT:
A couple of other options.
Go to a food court like the one in Town Hall Square. You can plant yourself in a seat with a nearby wall socket and work away. Should be reasonably quiet at that food court.
There are also a few good cafes that fit the bill around Haymarket, like the Starbucks on George St near Capitol Square, Gloria Jean's on Pitt St, etc.