Inspiration here, here, and the original.
Put down my prefix.
Put on my suffix.
You can't see my infix for the trees.
If I had a cape, it would look like this:
Image from benjamindavidsteele.wordpress.comWhat am I?
Hint #1:
If I were an an island, I'd be nominally in Auckland.
Hint #2:
The answer is suggested by the title.