[danik.js]

<select name="select">
<option value="1" data-city="Москва">1</option>
<option value="2" data-city="Казань">2</option>
<option value="3" data-city="Уфа">3</option>
</select>
<div id="gorod"></div>
<script src="//code.jquery.com/jquery-latest.js"></script>
<script>
    $('select[name="select"]').change(function(){
        localStorage.option = this.selectedIndex;
        $('#gorod').text($(this[this.selectedIndex]).data('city'));
    });
    if (localStorage.option !== undefined) {
        $('select[name="select"]').prop('selectedIndex', localStorage.option).change();
    }
</script>