SLOWHATCH, I don't know whether your signpost is the other side of #2 of the screencaps (I think it probably isn't). Anyway, for #2, there is no possibility that the signpost is in Christchurch. Follow this logic:
1. Given the larger distance to Sydney(2169 km) than Melbourne(1682 km), the place must be south of Melbourne to make that so.
2. The only place in Australia of consequence south of Melbourne is Hobart and that is far too close.
3. That leaves only New Zealand as a possibility.
4. My world distance calculator gives these distances:
Auckland to Sydney 2151 km Auckland to Melbourne 2614 km
Christchurch to Sydney 2123 km Christchurch to Melbourne 2387 km
5. To Melbourne is too high, so we need something southwest of Christchurch. There is only one major airport that fits, Queenstown, where AR2 did some bungee jumping and other extreme sports. I haven't found a distance calculator that includes Queenstown but a rough approximation of how much the distance is to Melbourne should be in the right ballpark.
I have discovered a signpost in Auckland airport that looks totally different and it states Sydney 2159 km.
I have also not been able to discover any signpost at the Queenstown airport so far.
I have done an approximation of the lower distance that Queenstown would bring from Melbourne compared to Christchurch. It would be less than 400 km and I need a reduction of about 700km.
For purposes of validating what I was doing I tried Dunedin airport, southeast of Queenstown. It gave results of 2087 km to Sydney and 2253 km to Melbourne.
What I believe this shows is that there isn't going to be any airport on New Zealand that will be able to approximate the required 2169/1682 from the signpost. The only spot which would have those distances would be in the Tasman Sea off the west coast of the South Island of New Zealand.