I've only been to the North Island, but there are a few parts to an answer:
1. If roaming charges are high, consider buying a local SIM card instead, e.g.
https://toomanyadapters.com/buying-s...d-new-zealand/ You'll need what the US calls an "unlocked" phone or what is common in other parts of the world, a phone not tied to specific service.
2. I don't have a shortcut to asking for hotel availability, but an offline site like MAPS.ME can at least tell you locations of such hotels. Sometimes I'll turn up at one and if they are full, ask for suggestions. That works if I'm not in a peak period and if the place is populated enough to have multiple choices. At times I've done a hybrid - made reservations in advance for a spot I expect could be tight (e.g. make reservations using wifi/expedia the night before) and let it float in other areas like larger cities where I expect plenty of choices.