Which Hawaiian Island?

I'll be in Hawaii in July, for the first time. I'll be on Oahu for a
week for work, and I'd like to take another week to explore another
island.

I enjoy hiking, beautiful views (for photography), and non-tourist-trap
things. Which other island should I concentrate on? Based on what
I've read, I'm looking at the Big Island or Kauai, but I'm wide open to
other suggestions. What is worth doing on your suggested island?

And on Oahu, what should I do? I will definitely see Pearl Harbor, but
the rest of my evenings are open.

Thanks!

Sarah