Recently I have heard movements from the local stores (say clothes, electronics, foods, etc) and some politicians (of a particular wing) that argue that you should buy in local, small stores. Appealing to a feeling of nostalgia, they say those stores have been there for a long time and now running away from them is not the best thing to do.
A quick search for the keywords
compra en la tienda de barrio which roughly means "buy in local stores" cite some reasons like helping the local and familiar economy, less pollution, customized attention (taken from here, in Spanish). Beside the fact that these reasons are at best questionable, the purpose of every buyer is to maximize savings, one way or another.
Say for example, Amazon usually offers you a better deal on a home appliance or a phone, way better technical support and extended warranty than a local store, or a supermarket chain that can deliver your fresh meat and groceries within two hours or in an allocated time slot, instead of going all the way to the local store to buy the goods. These, amongst other reasons, are crucial for buyers. Then, my question arises: from a buyer's economic point of view, what would be a good reason to keep buying local?
If location is needed, I'm in Spain but the answer could be related to other locations.
EDIT: Both answers received so far are pretty good and they make a good point. However, I can't help but notice that they are pretty related to small towns, rural areas or to some extent, a remote place where the vicinity of the local store poses an advantage to the big companies. My question was more aimed towards a medium-to-big city, where this vicinity is not much of an advantage. Please keep it in mind when answering.