Hello @phoebeghostwriter. There are some very small stores near where you are staying but they do not carry much. People's Co-op is the closest full service grocery store near you. The Co-Op is 1/2 mile from your hotel on 6th St. SW and Broadway. It's an easy walk so long as you aren't carrying heavy bags of groceries. Actually, the Co-Op was where I go most often. I see others suggest the Hy-Vee Grocery Store. This is the big grocery store (several locations) in Rochester. The closest Hy-Vee to Mayo Clinic is on Civic Center Drive and 6th St. NW - too far to walk but they do deliver or you can pick up curb-side. Ask for a map of the local area at the Kahler Inn.
https://www.hy-vee.com/stores/detail.aspx?s=146
I was in Rochester for 6 weeks and stayed in a long-term apartment. I had my own car. Even so, I had lunch in the Mayo Clinic Café at least 2 or 3 times a week. The meals are nutritious , tasty, and very affordable. It really is the safest (in terms of COVID) place to eat in a cafe in Rochester in my opinion. I spent on average $7.00 for myself. This was my "treat" to myself after radiation therapy. There is a Caribou Coffee place right in your hotel. There aren't any grocery stores in Mayo Clinic but you can pick up sandwiches and small items in the Gonda Gift Shop (there's a small café there).

You'll find everyone at Mayo Clinic to be very helpful. Ask anyone there for directions within the Clinic and if you look the least bit confused someone will stop and ask if you need help.

I hope your flights are on time and your appointments at Mayo go well.