Have you heard of this miraculous thing called public transit? And there are things called panniers which are pretty cool too.
But frankly, if you don't have groceries within walking distance, your neighborhood and your zoning laws are very poorly designed.
And that's deliberate. Neighborhoods around the world are designed to require cars to live in, because of oil company lobbying, and also for "security", in order to keep out people too poor to own cars.
Getting rid of cars requires changing the various ways our cities are designed to make cars necessary. That's worth doing too.
Living outside land of the free, I have like 4 grocery stores and 1 supermarket within 15min walking distance, and I don't live in a dense neighborhood.
I used to live in a place that was somewhere between suburb and rural and I loved not being around people but I hated not being able to walk to get basic necessities. Now I live in the city and I have everything I could ever need within a 15 minute walk and I get to choose whether I pay for a car, a licence, plates, insurance, gas, maintenance and repair. This system really has us fucked into believing that this is the way it should be.
A few streets on a mountain can and should have a grocery store. For the occasional specialized needs, rural residents can use comparatively inefficient modes of transport because of their relatively small number. There's still a huge margin for better efficiency and planning.