サーバー側への Ajax 呼び出しをセットアップして、写真のパスとテキストを取得できます。このようなもの。
$(function(){
function FillDivAtRandom(current){
setTimeout(function(){
//pass the current place to explore id to the server so you don't get the same back, if none then return anyone.
$.post("http://americanart.si.edu/Request/PlacesToExploreNext", current, function(data){
//fill the div with new data return from server
//you don't seem to have an ID on that div or elements so put one on it first then use it as a selector
//set the image
$('#placestoexplore_image').attr('src', data.image);
//set the text
$('#placestoexplore_description').html(data.description);
});
//call the function again
FillDivAtRandom(current);
}, 10000);
}
}