@bevprescott - I just had my liver transplant at the end of Dec 2023, and we wondered the same before getting the call.
We ended up staying at the "TownePlace Suites Rochester Mayo Clinic Area". I'm not comfortable doing Airbnb/VRBO rentals, so the extended stay hotels were what we looked at. It's not the cheapest option, but it didn't break the bank either. Try calling them directly and telling them your a Mayo clinic patient - some hotels will give you a discounted price if you talk to a manager when booking.

Also, check if your insurance has a reimbursement for travel expenses related to transplant. Suprisingly, mine had a $10k lifetime max benefit for hotel stays, car mileage & parking fees that I could submit. It was a very hidden process that I had to mail in paper receipts and fill out a paper form that looked like it was a crappy 6th or 7th generation copy of a copy of a copy that someone had gotten from a past coworker who retired in the 90's. Anyway, it worked and I got a partial reimbursement (max of $50/day) for hotel costs, which didn't cover all my costs, but was far better than nothing! It's worth calling your insurance co to ask, just in case!