Depends on what sort of phone line access you'll have. If you're saying in hotels/motels then they'll most likely charge you per minute for using the phone even if it's a local call to an ISP.

You can find wireless most places, but rural areas you might be hard pushed to find any access. Not to mention you might be paying $10 an hour or something for some commerical hotspots.

All dialup ISPs are pretty much the same these days in NZ, personally I'd go with ihug - welcome to ihug!, I've used them before for dialup (abiet 5 years ago before broadband, but still). Looking at $24.95 a month for unlimited dialup with ihug (unless you switch your tolls over to them, which you may not be able to do).

Hopefully this has helped you out a bit.