It never actually says— I'm sure they don't have a country (or countries anymore), or 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 europa area would be too small to fit the walls's whole area and it also said that that some areas and animais shown in the OVA where they had a training assignment are exclusive only to America . But it's still just a fã theory . Maybe the author will reveal it sooner or 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 .