I stayed with residents at most of my clerk months. I found that through the clerkship coordinator or direct via residents/networking.
I think I did that 3/5 clerkships, and the other 2/5 had free hospital-arranged housing in dorms or whatever. My school didn't do core rotations and has all of that med/surg/ER stuff local to the school during 3rd year.
I did the same for clerks at my program when I was a resident (both core and month)... rented them a room for a fair price. I got a lot of offers for LDS teachings lessons out of the deal
A lot of the better programs that have clerk/core students every month have at least one or two residents who have a rental or purchase house bigger than they need and use it for that purpose. Some residents do it by design from the start, others just realize you're never home as a resident and they don't need the space, and others (me) have things change with roommate leaves, divorce/separate, etc. It ends up win/win for sure... cheaper than hotel or BnB and helps the resident pay rent also. As was mentioned, you just ask the clerkship coordinator or program admin assist. Even more valuable than just saving a couple hundred bucks, you can
get good insight from the resident on their program and the city by staying with them, meet more people, find the occasional good party, etc that way. I took some of the clerks with me to the parks, gym, shooting range, downtown, meet-ups with other residents, etc etc that they might not have found on their own.