About workout facilities:

Mayo has an employee only workout facility, https://dahlc.mayoclinic.org/. I do not think public or patients have access.

A few options if need a work out facility are Y and LIVE 125. Not sure if have temporary memberships. YMCA has a location near downtown Rochester. Older facility, but has exercise equipment, pool and classes. Another option is 125 LIVE, bigger newer facility on north end town. The Y is not as crowded as LIVE 125.

For short term I suggest the Y - https://www.ymcanorth.org/ , you can contact about short term membership.

If have a car and feel like site seeing while here, the first week of Oct, there is a Fresh Art tour across Mississippi in Wi. It is mon of my favorite things to do in fall. Local artist have open houses in studios and shops in small towns. If follow map and signs, it is beautiful drive along Mississippi river. See web site for more info: https://www.freshart.org/ . I always cross river in Wabasha MN, it is decorated for fall,.
Good luck with visit.
Laurie