If you want to travel around Sydney without a car, what kind of public transportation is usually used? Is there also a free bus like in Melbourne's city? If there is no free bus, do you need to buy a transportation card ?

There is a free area, a small piece in the city center, you still need to buy Opal card Daily and weekly limits

Subway and ferry are very convenient.

Buy Opal card, capped at $2.80 on Sundays, valid for all modes of public transport including trains, buses, light rail and ferries.

Buy a card, but the transportation fee for 1-6 in Sydney is very expensive, and there is a discount on Sundays.

Don't take the bus, they don't announce the stations. Light rail is still okay. On Sundays, you can ride for 2.8 yuan.

Buy a bus card.