Here is my itinerary for my Sydney trip. Please give me advice if possible.
Day 1: Reach Sydney around noon. Plan to rent a car and drive to Blue Mountain and stay there for the night.
Day 2: Explore Blue Mountain and Jenolan Cave and back to Blue Mountain to stay for the night
Day 3: Drive to Wollongong and back to Sydney.
Day 4-7: Explore Sydney City
Is this feasible?
Sounds all right. Some bigger considerations:
1) If you're arriving on a weekend, might be better to do the markets first. Cos the main markets which are clustered near or in the city: Eveleigh Markets (for organic farmer stuff), Paddington markets, Rocks Markets only open during the Sats and/or Sundays.
2) The road from Katoomba to Jenolan caves can be quite difficult and winding drive, so you may want to take it slowly and rotate drivers esp. after a long 8 hr flight and +3 hrs jetlag .
3) If you're using a GPS, be careful not to take the fastest and shortest route to Wollongong. IMO, there's nothing much in Wollongong; is just a bigger city with more people. You would want to explore the surrounding areas by the coast nearer north and south of Wollongong. GPS usually route the inland Hume highway A31, that bypasses the coastal attractions. To avoid that, key in the coastal attraction directly (for example sea cliff bridge) and not Wollongong, and let GPS route using the coastal road which branches from the M1 highway. It's advisable to do the coastal scenic drive on your way to Wollongong and not on your way back to Sydney. The attractions are more accessible southward than northward.
Also, if you're driving from blue mountain, you may be routed to M7 or M5 (which are both toll roads) to M1. Not to worry, you can just drive pass but remember to login to etags website to pay for the toll before you return the car. Otherwise, you will be slapped with a heavy administrative fine.
4) Coastal road is winding and cuts across national park. It is called the Grand Pacific Scenic drive.
4) gobirds.com.au is a good rental car company to use.