No, Walmarts aren't everywhere. Each area of the country has their own set of stores.
There are other ways to get free special pets. The Twitter announcements have given out some I have heard through the gossip loop, and you can get them by buying a magazine (which can be gotten online).
Everyone will have their own way of getting pets, and to try and make our characters our own and unique it is good that there are varied ways for people to be such.