Well, I live in Melbourne, so that half of it I don't need to research!
Melbourne has lots of beaches, but they are on the inside of Port
Phillip Bay, and there aren't any waves happening. For surfing you
need to drive about an hour from downtown Melbourne.
To the west, just past the city of Geelong are surf beaches around
Torquay like Bell's Beach and Jan Juc, and many other little spots
along the coast. Some big tournaments happen at Bell's Beach, and part
of the movie Point Break was filmed there. The international surfgear
company Quiksilver started life in Torquay.
To the east is Portsea. Between Portsea and Melbourne is the
Mornington Peninsula, and houses pretty much line the entire journey -
you could live at any point between the two.
To get out of Melbourne takes about an hour in most directions, it is
a very spread out city. I have been camping and hiking at various
spots within 1-2 hours drive. My favorites are the Grampians, 260km
from Melbourne, and Wilson's Promontory which is a bit closer. Winter
skiing is within 2-3 hours drive.
You can live in Sydney and at a surf beach at the same time. Popular
surfing spots within the city of Sydney are Bondi Beach, Coogee,
Tamarama, Cronulla and Maroubra. To the north is Manly and many
Bondi & Coogee Beaches - Sydney Visitors Bureau
Thirty kilometres south of Sydney is the Royal National Park, a good
spot for bushwalking.
Ninety minutes west of Sydney is the Blue Mountains. They are very
popular with locals and tourists alike. The main activities are hiking
The best skiing in Australia is within the Snowy Mountains. To get to
the good ski fields like Perisher and Thredbo from Sydney is about a
5-6 hour drive.
If you are trying to work out which city to live in, try them both for
a week, and try Sydney first. Although they are more or less the same
size, Sydney is relatively hectic and Melbourne is relaxed. Sydney is
flash and Melbourne is cool. Sydney has quite good weather, Melbourne
has "four seasons in one day". Today it is 37 degrees in Melbourne,
yet last Xmas day it was too cold and windy to hang out on the beach
in the afternoon...