If you look on Google maps, look for Port Campbell National Park. Look for the 12 Apostles parking area (intersection of the Great Ocean Road and the very small Booringa road, about 11 KM East of Port Campbell).
About 5km East of the 12A parking lot, is a dirt road that leads down to the beach. This may be the closest spot to get to the surf. I'm not sure if it's advisable, safe, or even legal, but a sea kayak from this spot would be awesome.
(I'm guessing on this one...) about 2km West of the main parking lot is a turnout. There is a path here that after a short time should give nice view. The path continues East for a long time and eventually looks like it meets another that goes down the the beach. I doubt you can see the 12A from there though.
If anyone knows about the safety, legality, etc. of sea kayaking in this location, please let me know.