The best time to go is actually the afternoon/evening. You get a spectacular sunset view and then also get to see the city at night.

Being Winter, it will also mean it isn't too hot (climbing the coathanger can be hard work, especially in the jumpsuits you wear).

In my experience (personally climbed once and known heaps of other people who have) they best timeslot to aim for is the last one before the official "sunset walks" begin. You'll still get to see the sunset, but pay quite a bit less. Double-check the expected sunset time for the day you're looking at - it takes about an hour to get to the top, then you'll be up there for about 30-45 minutes, then another hour to get down. Also shoot for mid-week, as weekends tend to be busy.

Finally, wrap it up with a beer or three at the Harbour View Hotel, just 'round the corner .