Так?
<!doctype html>
<html>
<head>
<meta charset="utf-8">
<title></title>
</head>
<body>
<input id="city" size="30" /><br>
<div id="info"></div>
<script>
var div = document.getElementById('info'),
input = document.getElementById('city');
input.addEventListener('keyup', function() {
div.innerHTML = this.value;
});
input.addEventListener('focus', function(e) {
div.style.visibility = "visible";
});
input.addEventListener('blur', function(e) {
div.style.visibility = "hidden";
});
</script>
</body>
</html>