JSFiddle - React, Tailwind, and code Playground

HTML

<select name="selectlist_city" id="selectlist_city">
    <option value="">Select city</option>
    <option value="Arendal">Arendal</option>
    <option value="Fannrem">Fannrem</option>
    <option value="Molde">Molde</option>
    <option value="Oslo" selected="selected">Oslo</option>
</select>

<div id="city_list">
  <div class="list textfield50pc"><ul>
    <li class="city Molde"><a href="#">AMFI</a></li>     
    <li class="city Oslo"><a href="#">Arkaden Shoppingt</a></li>       
    <li class="city Arendal"><a href="#">Maxis senter</a></li>
    <li class="city Fannrem"><a href="#">Mo Marked AS</a></li>
    <li class="city Molde"><a href="#">MoldeTorget</a></li>
    <li class="city Oslo"><a href="#">Oslo City</a></li>
    <li class="city Oslo"><a href="#">Paleet</a></li>
    <li class="city Oslo"><a href="#">Veitvet senter</a></li>
    <li class="city Oslo"><a href="#">Vika Terrassen</a></li>
    <li class="city Oslo"><a href="#">Westside Senter</a></li>
  </div>
</div>

CSS

#selectlist_city {float: left; }

 #city_list { 
    margin-left: 20px; 
    height: 200px; 
    overflow: auto; 
    border: solid 1px #D1D2D1; 
    background-color: #fff; 
    padding: 5px; 
    width: 250px;
    float: left; 
 }

 #city_list .list .city { display: none; }

 a { color: #0087D5; text-decoration: none; }
 a:hover { textdecoration: underline; }

JavaScript

//On page load, lets see if a city is selected
var shmall_selected_city = jQuery('#selectlist_city option:selected').val();

if (shmall_selected_city.length > 0) {
    jQuery('#city_list .list .' + shmall_selected_city).fadeIn('fast');
}

jQuery('#selectlist_city').live('change', function() {
    shmall_selected_city = jQuery(this).val();

    jQuery('#city_list .city'). fadeOut('normal'); 
    jQuery('#city_list .' + shmall_selected_city).fadeIn('normal');
});