Yes, many of the hotels are connect to the clinic via the Subway (underground walkway). It’s so convenient because you’re never outside to face the elements. You don’t have to worry about finding parking spots for your appointments or have to wear jackets. It’s easy to duck back to your room between appointments. Often there are rooms with kitchenettes or even full kitchens.
We always stay at the Marriott Residence Inn. It’s 2 blocks west on the Clinic on Center street.

Take a look through this discussion for some ideas.

Which hotels at Mayo in Rochester are connected to skywalk/subway?
https://connect.mayoclinic.org/discussion/hotels/
It would be good to book soon. I’m not sure how many days you may want to plan on staying. Sometimes appointments may be added to your schedule once you meet with a specilist.
But most hotels are fairly flexible with extensions and cancelations.