One thing that always amuses my Eastern States friends is our tendency to refer to the entire other half of the country as "over east". Sydney? Melbourne? I dunno, it was somewhere over east anyway.

Edit: I had 'over' for both east and west, but there's nothing but ocean to the west of here so we don't have much occasion to talk about things being to the west of us... apart from Rottnest Island, which is still 'over' because you get there by boat or plane.

The area I'm in is often referred to as the 'High Country' so that probably explains the up and down idea. I'd still go 'up' to Auckland because it's north, even though it's at sea level.

I use over to refer to towns on the other side of the river from here. You also go over to people's houses. I guess I use out but it has no direction associated with it. It is more related to remoteness from things. You go out to a farm and in to town. Over the river. Down to the city then back up to home.

In Perth people often would say they are "going over" to Melbourne or Sydney. There is also the reverse "coming over"

"Out" is used generally such as in "heading out" where often no destination is specified. Also we sometimes use "outback" meaning anywhere not in a city or suburban area.