I believe for every city performers get the choice between an arranged hotel or a Per diem to use on finding their own housing. Sometimes many cast members will chip in their per diem to share a nice AirBnB or just stay in the hotel. It usually differs for every performer and city.
I believe Equity has to provide a hotel/accommodation with a kitchen in the room as well. My non-equity friend was doing a show with some Equity members in the cast and as a result they all got mini suites for their month-long run as a result. Some touring/regional venues have "dorms" that meet Equity standards and those are sometimes offered to cast/crew depending. I follow some actors on Instagram who are on tours and most seem to get AirBnBs these days. I know some people who made a considerable amount of money (enough to buy apartments) by touring for a year and splitting rents with other cast members and basically saving their per diems.
In the UK actors find accommodation themselves. Whether it be through an AirBnB, a hotel or something else they get a weekly allowance between £180 - £250 a week to live on.
I rent my spare room out to actors quite regularly through the facebook group Theatre Digs List. I’ve currently got the company manager of Rocky Horror in my spare room and next week I’ll have one of the ensemble members of Amelie.