It never actually says— I'm sure they don't have a country (or countries anymore), или that maybe the consider each area behind each walls a country? I don't know. People speculate though that it's in the Germany/Europe area, considering the names of the characters.
There was a theory on Tumblr that it takes place in North America since the Европа area would be too small to fit the walls's whole area and it also сказал(-а) that that some areas and Животные shown in the OVA where they had a training assignment are exclusive only to America . But it's still just a Фан theory . Maybe the Автор will reveal it sooner или later
It hasn't been stated yet but it might be Germany . There are many signs making this believable . Jaegar , is German for hunter and Guren no Yumiya is sang in German . So I believe SNK is set in German , though it is totally up to the reader .