Don't have an exact lat/lon, but this is roughly centered on the summit: Google map. Guess lat=-42.94 lon=171.54 would work.
As a general statement, NZ campervans are free to camp anywhere except where posted. There are numerous spots around town. Visitor Center would work. There's a great spot at the trailhead for the Mount Beelah track, just a bit south of the visitor center and a short distance up the road toward the police station.
In addition to the Avalanche Peak Track and Scott's Track, I know of two more routes:
Andre, someone has mistakenly made this page PARENT of the Southern Alps instead of a child. As a result, the Southern Alps are a child of Avalanche and show up as a sub-range of Avalanche Peak! You can easily fix that. So could the Southern Alps page owner, but he's long gone from SP.
Now it should be fixed! Many thanks for making me aware :-D
Please include the following coordinates so that this page appears on the map. Thanks!