Yes , I have lived in Sydney most of my 60 years and are glad to help.
Just note , I haven’t ever taken the taxi. I much prefer the train.So I’m just guessing.
1. The airport to the Rocks is probably about half hour by taxi.
2. Taxi will cost about $50
3. The Rydges is about 100 meters ,it’s the closest hotel. It used to be a holiday inn so only about 3 star but very popular with cruisers.
4. Rydges is right in the middle of the Rocks , the main tourist area of sydney. Lots of places to eat, shop and take your money.
5. You can use your credit card everywhere, even on public transport .
6.Its up to you if you want to get local cash ,a lot of people here don’t have any cash .My daughter gives me a dumb look when she sees cash .
I like to have a little but I’m a bit old fashioned. You can always give it to your cabin attendant as a tip .