Yes you prob picked the worst area for coverage low population = low coverage
4G rural you need 700 Mhz city 1800 Mhz in general
many rural areas do not have 4g yet
enjoy your trip and dont worry about phones !
Prepaid Sims
Spark NZ, Skinny , 2 Degrees , Vodafone NZ and Australia, EE UK , Travel Sim , Plus Poland
Phones:
GSM: Nokia 5110 , 6110 , 6310i ,
UMTS - LG P970 ZTE R54 Galaxy Mini Samsung GTE3210
LTE 4G / 700Mhz Samsung J1 and J 2
LTE 4G / 1800 Vodafone 890N . Samsung Tablet
CDMA: Nokia 6385 ( now dead )
TDMA / AMPS Nokia 6120 ( all dead )
SMS contact and Tests +64 20 4577475