you can pick a spot on the moon that gets sun in which case nighttime is only ~1.6x colder than the coldest recorded temperature in Antarctica! (but day is ~1.8x hotter than the hottest day on earth.) or: always night, where it's ~3.3x colder than Antarctica. dealer's choice
building a city in antarctica is orders of magnitude easier, cheaper, and safer for its inhabitants than building a city on the moon