Hi, @johnbishop had great ideas for grocery stores. There is also a Fresh Thyme store about 3/4 west of the clinic. However your best bet if you don’t want to walk or take an Uber is have the groceries delivered.
Hi-Vee grocery has delivery.
https://www.hy-vee.com/stores/Detail.aspx?s=143
Mayo doesn’t have a food store but there is a cafeteria off the Gonda foyer. It’s one of the main buildings you’ll be passing through daily. You could grab food to go.

Also, there are no shortage of great restaurants in Rochester and most have delivery available.
Some of the restaurants and the mall with a food court, are also connected via the Subway system (the tunnels) to the clinic so you’re not walking outside.
Many of the hotels are equipped for long term stays with kitchens or kitchenettes with a refrigerator, stove and or microwave.

I see you’re staying at the Kahler so you’re very close to several of the restaurants.
As you can tell, a lot of us are familiar with staying near the Clinic so don’t hesitate to keep asking those questions! ☺️ You’ll be a pro by the end of your visit.