Public Transport Trip Planner
A good website that helps you plan any trip from point A to
point B by selected modes of transport. It will tell you what bus, train or ferry can get you there and all the details.

Ferry
Sydney Ferries
You can catch a ferry from Circular Quay to get to the start of most of our paddles.
The State Transit ferries don't run to Lavender Bay but you could catch one to Luna Park(Milson's Point) and then it would be just another 10 mins walk around to Lavender Bay wharf. These ferries leave from Wharf 5, Circular Quay and you can catch the Balmain, Woolwich (Hunters Hill) or Rydalmere ferries as their first stop is Milsons Point.

(Note: the timetables on their website can be slow to load). You could ring the Transport Infoline on 131500 and they will can give you all the info.

Bus
State Transit Bus Timetables
Alternatively ring the Transport Infoline on 131500. Note that this doesn't include all bus companies. Try the Public Transport Trip Planner as that includes them.

Train
CityRail Timetable Menu
Trains run from the city to North Sydney constantly so you don't need to consult a timetable unless you are coming from further afield.

Taxis (Cabs)
If you catch a taxi to Lavender Bay be careful as most drivers won't know where it is. You need to ensure they take you to Lavender Crescent which comes off Lavender Street.

Taxi Fare Calculator 
This will help you estimate the cost. Not sure how accurate it is but it gives you a decent ball park figure. Fares would vary slightly between cab companies.

Silver Service Taxis
TEL: 133 100

Premier Cabs
TEL: 131 017

RSL Taxis
TEL: 9581 1111

Lime Taxis
TEL: 13 5463

Legion Cabs
TEL: 13 1451

Taxis Combined
I could not recommend strongly enough against using Taxis Combined. They have caused me to miss flights and failed to arrive altogether when booked. Terrible service.