Brian, I love your idea of monthly meetings aiming at visiting every café in town!
Yes. nothing here open 24 hr except (perhaps) MacDonalds. People on TripAdvisor often ask where to get a meal after 9pm. There are a few places in the city centre that open very late (like 3 or 4am)on Friday and Saturday but I do not know how late they serve food, usually they close the kitchen about 9pm.. But we only have a population of 135,000. Auckland with over a million may have more open.
When I took over the 60 Plus hiking group six years ago, we began going for coffee afterwards, actually some of us had started doing that beforehand but the previous leader was not impressed. There are lots of groups in our 60Plus club, one is called 'Coffee & Culture' and, after a monthly visit to a museum or art gallery or similar, we go for coffee nearby. Another is the 'Movie Club' and after our monthly movie on Sunday afternoon, many go for coffee but always the same cafe. So I suggested a 'Just Coffee' group. It cannot be openly advertised in the club as most cafes cannot handle much more than dozen. We have had between 4 and 14 but usually between 6 and 10. I advertise by email the Saturday before (it is on Thursday or Friday at 10.30am) and ask people to let me know if possible the evening before. If 6 or more, I ring the cafe early and book a table. Today, after the supermarket, I went to 'Muffin Break' which is in the Food Hall and had a mixed berry muffin (my favourite) and a medium cappuchino. While not strictly a cafe, I go there a lot as every 5th coffee is free and they give me a free muffin in the month of my birthday..