In your situation I would probably order my weekly groceries online, if that was an option. I would still visit the grocery store occasionally, in which case I would walk and/or go by bus. Well, in reality I would probably own a bike, but that also depends on your infrastructure over there. I’ve never lived that far from the nearest grocery store, though. There are many options here within that radius, the nearest ones being basically next door.

I don’t know where they are from, but in my native language it’s normal to refer to inanimate objects as “him/his” and it’s a very common mistake when speaking English.