Hi Conrad,
Aside from internal linking, it is also important to look at the page titles, and these could do with some work.
When crafting page titles, you want to remember that Google has changed how they calculate how much is now shown, and this equates to 56 characters (512 pixels). MOZ has a tool to show you what would be seen here.
You say that when someone searches for "active new zealand", then you want this page to be returned http://activeadventures.com/new-zealand
However, the page title of that page is "New Zealand Hiking & Adventure Tours & Vacations | Active Adventure".
This title is also a little spammy, and you need to get your desired phrase in there as well, if you can. Rather than what is there, I would have "Active New Zealand adventure tours | Active Adventure". This gets both key phrases in and fits into the 512 pixel limit that Google now has.
Internal linking can also help by explaining more to Google about the pages as well. A strong anchor text around each phrase would be desirable here.
If you want a hand with any of this, just drop me a PM and will be happy to give you some pointers.
-Andy