You don't need an alternate just because the destination only has a GPS approach.
Are you sure. I think a tech alternate is require for a destination with only one type of approach available.
Yes, I am sure. 19.207 & 91.405 refer. (Part 135, my memory fails me.)
As to the availability of VORs, yes, I did forget about the Sth Island West Coast. If you work there, you'll likely be a VFR. But if IFR, you'll need ADF on the IR.
As to Northland, I planned to fly GPS approaches and was able to nominate ILS or VOR airfields on the rare occasions I needed an alternate. Worked for me, although I did have ADF as well.
Horses for courses anyway, the OP should get what he/she can afford and needs.