problems reading ajax array

It's an arrangement of objects, not an array of strings, try trying this

$.ajax({

   type:"POST",
       url:url2,
       data:{code:code},
       datatype:"json",
       contenType: "application/json",
   }).done(function(response){

       var text=response;
       var obj=JSON.parse(text);


       obj.forEach( ciudad => console.log(ciudad) );



       //Suponiendo que el nombre de la ciudad este en una propiedad llamada nombre
       obj.forEach( ciudad => console.log(ciudad.nombre) );

}

You are returning an array of jsons, when you iterate over the json array, each element is a json.

In for in javascript iterates over the keys , that is, each you use the for (var propiedad in obj) {... , propiedad will be worth the key , which is not implicit, take the number, ie 0,1,2,3 ... etc

Then as propiedad = 0 , when doing obj[propiedad] , that is to say the index 0 of propiedad , the resulting value is {"nombre":"Kabul"} . This means that it is indeed an object.

To access that data, you simply have to access that property so obj[propiedad].name

for (var propiedad in obj) {
  if (obj.hasOwnProperty(propiedad)) {
    console.log("En la propiedad '" + propiedad + "' hay este valor: " + 
    obj[propiedad].name);
  }
}

In this option it would be worth checking if from your php it is necessary to return it as a json array instead of an array of only the names, which you could do

$ data = array ();

 while($row= $stmt->fetch()){ 

     $data[] = $CiudadNombre;
 } 
 echo json_encode($data);

and then you could show that info with the for of javascript as you have it now.

If you want to have a json array and iterate over each one, you would have to put another for in your json for now iterating over the json object as such