By the way, monasteries existed long before the Benedict order, and other orders existed in parallel. Some monasteries did not welcome visitors, especially women and couples.
You're making this seem misogynistic, but indeed, typically female monasteries were not (and are still not) open to men.
You're not wrong I was incomplete in my previous statement. Monasteries would often try to render assistance to the exceptionally needy, but have historically operated as regular inns only for those who could stay within the convent walls. This was basically restricted by sex. Even today, if you're going to do a retreat at a monastery, couples typically would have to stay away from the cloister (many monasteries - but not all - offering retreats typically have a separate house for these individuals, a short distance from the main cloister). Only single men would be permitted into a male monastery (behind the cloister for the night) and single women to a female one.
Re the paying stuff. As far as I'm aware (and I've researched a few monasteries in my area and know several monks), the payment is a suggested donation, not a requirement. Of course, that's my own anecdata. I would be interested in knowing if there is a monastery charging for the actual stay, because typically they're not supposed to.