I rarely visit family owned stores (including convenience stores). For one thing, I can usually find the lowest prices by shopping online or via scanning the aisles of big box stores. At the same time, I prefer a) to maximize my choices and b) to remain anonymous. I can serve both needs by shopping at a large establishment or by purchasing goods online. I do occasionally patronize a family owned restaurant or two (technically, a McDonald's is family owned if the franchisee only owns one or two restaurants), but that is a different matter.
I had a gift certificate (not a gift card but an "old timey" gift certificate) to a small family owned men's clothing store in Roanoke. I went in to the store and was reminded of the potential benefits of shopping in these family establishments. The storekeeper was more than happy to show me what he had to offer. More importantly, he did not try to rush me or to convince me to purchase anything. He even agreed to cut the price down on one of the items I had purchased. I felt like I was talking to an old family friend as opposed to a non-caring store employee.
Granted, I sometimes have the same experience when shopping in large department stores or at discount centers. Nonetheless, I think I would more consistently have this experience if I shopped at small, family owned establishments. With that being said, I will continue to spend most of my shopping time online or at major retailers; however, perhaps I will dedicate a little more of my shopping time to the family owned establishments, especially when the items I need are relatively inexpensive.