In most places, owner permission is sufficient to locate on private property; however, there are exceptions (notably, HOAs). Do what diligence you must to feel great about proceeding.
If you decide you want your municipal entity’s go-ahead and/or your dream location is on city property and you don’t have an inside contact (start there if you do!), go to your city’s website and find “permitting.” Select the permitting type most like a mini pantry.
Here the menu item most like a mini pantry is “Tactical Urbanism.”
Find a phone number and call it. If there is an online form, fill it out also. Ask for advice rather than permission. Do both again the next day. Wait a week. Repeat. Be persistent, and be prepared with answers to questions about liability and safety, right of way, and maintenance. Soliciting city involvement will make implementation more labor and time intensive. The tradeoff is good community buy-in prior to launch.
Keep in your city’s good graces by steering clear of easements and the apron between the sidewalk and the street.
Again, most places will welcome your mini pantry. Should you run into difficulty, take a look at Little Free Library’s How to Deal with Zoning Laws, Municipal Regulations and HOA Rules and How Deal With Zoning Regulations—Spencer’s Story. And please contact us to let us know about your experience.