We often don't get a choice of when we fly, but if you do have some flexibility, picking the right day can make a big difference. It's well-known that mid-week flights (Tuesdays to Thursdays) are often the cheapest, but if you have to pay full fare anyway, then picking a less busy day of the week can make the flight experience less stressful.
Degrees of activity vary widely between cities. Sydney's domestic airport is pretty much a ghost town on a Sunday morning, but flying out of Perth yesterday, the check-in queues extended past the door. Staff told me that Saturday is the quietest day at Perth (though that's not saying much apparently). Let us know what days work best for you and we'll compile a handy guide for the weary local traveller.