Check out www.nswkba.com.au Its got maps of all spots in and around Sydney and NSW.
-Brighton Le Sands is the closest to the city. Less affected by the tidal flow. It would take you about 20 mins from Bondi Junction to Brighton. Another 5mins to get to Dolls Pt. +20mins to Wanda,+25mins to Boat Harbour/Kurnell. There is also the Northern beaches great for wave riding.
As long as your safe and considerate Dolls Pt is fine, just listen to the locals advice. Pretty friendly bunch also.
Riding in winter is fine with a steamer. Coldest water I have kited in is 17-18 degs last July. Its not unbearably cold in my opinion just chilly.
From Sydney you can also travel 1.5-2hrs north to Central Coast or Newcastle. Aswell as 1hr south to Wollongong
I have never kited in Mebourne, I hear it is great! Although I've heard the water is much colder in winter, 12-15 degs.
I used to live in Bondi beach area, It sucks transport wise(traffic is a killer). The Junction is easier to get in and out of but living near the beach was a real hassle when catching public transport or driving in an out on a weekend.
All the best in your decision. Hope this helps PM if you have any other Q's
