var displayList = $('#display-wrapper ol');
var selectedOptions = {
    sortbyprice: '',
    rooms: '',
    region: ''
};


$('html').click(function () {
    console.log(selectedOptions);
});

$('a.region').on('click', function () {

    var selectValue = $(this).data('value');

    $('#region').text(selectValue);
    selectedOptions.region = selectValue;
    fetchDataFromServer(selectedOptions);
});

$('a.rooms').on('click', function () {
    var selectValue = $(this).data('value');

    $('#rooms').text(selectValue);
    selectedOptions.rooms = selectValue;
    fetchDataFromServer(selectedOptions);
});

$('a.sortbyprice').on('click', function () {
    var selectValue = $(this).text();

    selectedOptions.sortbyprice = selectValue;
    fetchDataFromServer(selectedOptions);
});

function serialize(options) {
    var arr = [];

    for (var key in options) {
        arr.push(key + '=' + options[key]);
    }

    return encodeURI(arr.join('&'));
}

function fetchDataFromServer(options) {
    $.ajax({
        type: 'POST',
        url: '/home',
        data: serialize(options),
        success: function (response) {
            if (response.error) {
                console.error(response.error);
            } else {
                console.log(response);
               
                updateDisplay(displayList);
            }
        },
        error: function (html, status) {
            console.log(html.responseText);
            console.log(status);
        }
    });
}

function updateDisplay(node, data) {
    var template = data.reduce(function (acc, item) {
        return acc + '<li><p>Region: ' + item.region + '</p><p>Price: ' + item.price + '</p><p>Rooms: ' + item.rooms + '</p></li>';
    }, '');

    node.empty();
    node.append(template);
}

#filter-wrapper {
    margin-top: 15px
}

#filter-wrapper ul {
    list-style: none;
    position: relative;
    float: left;
    margin: 0;
    padding: 0
}

#filter-wrapper ul a {
    display: block;
    color: #333;
    text-decoration: none;
    font-weight: 700;
    font-size: 12px;
    line-height: 32px;
    padding: 0 15px;
    font-family: "HelveticaNeue", "Helvetica Neue", Helvetica, Arial, sans-serif
}

#filter-wrapper ul li {
    position: relative;
    float: left;
    margin: 0;
    padding: 0
}

#filter-wrapper ul li.current-menu-item {
    background: lightblue;
}

#filter-wrapper ul li:hover {
    background: #f6f6f6
}

#filter-wrapper ul ul {
    display: none;
    position: absolute;
    top: 100%;
    left: 0;
    background: #fff;
    padding: 0
}

#filter-wrapper ul ul li {
    float: none;
    width: 200px
}

#filter-wrapper ul ul a {
    line-height: 120%;
    padding: 10px 15px
}

#filter-wrapper ul ul ul {
    top: 0;
    left: 100%
}

#filter-wrapper ul li:hover>ul {
    display: block
}

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<div id="filter-wrapper">
              <ul>
                  <li><a class="sortbyprice" href="javascript:" data-value="sortbyprice">Cheapest</a></li>
                  <li class="dropdown">
                      <a href="#" id="rooms">間取り</a>
                      <ul class="init" name="rooms">
                          <li><a class="rooms" href="javascript:" data-value="1DK">1DK</a></li>
                          <li><a class="rooms" href="javascript:" data-value="2LDK">2LDK</a></li>
                          <li><a class="rooms" href="javascript:" data-value="3LDK">3LDK</a></li>
                      </ul>
                  </li>

                  <li class="dropdown">
                      <a href="#" id="region">エリア</a>
                      <ul class="init" name="region">
                          <li><a class="region" href="javascript:" data-value="関西">関西</a></li>
                          <li><a class="region" href="javascript:" data-value="関東">関東</a></li>
                          <li><a class="region" href="javascript:" data-value="北海道">北海道</a></li>
                      </ul>
                  </li>
              </ul>
          </div>

          <div id="display-wrapper">
              <ol></ol>
          </div>

$('#room-filter').on('change', function() {
  const numRooms = $(this).val();
  $('.card').each(function() {
    if (numRooms && numRooms != $(this).data('rooms')) {
      $(this).slideUp();
    } else {
      $(this).slideDown();
    }
  });
});

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>

Rooms:
<select id="room-filter">
  <option value="">Show All</option>
  <option value="1">1 Room</option>
  <option value="2">2 Rooms</option>
  <option value="3">3 Rooms</option>
</select>

<div class="card text-left" data-rooms="1">
  <div class="card-body d-flex" id="content-card">
    <h2>Shack</h2>
    <p class="main-text">1 room</p>
  </div>
</div>

<div class="card text-left" data-rooms="1">
  <div class="card-body d-flex" id="content-card">
    <h2>Second Shack</h2>
    <p class="main-text">1 room</p>
  </div>
</div>

<div class="card text-left" data-rooms="3">
  <div class="card-body d-flex" id="content-card">
    <h2>Bungalo</h2>
    <p class="main-text">3 rooms</p>
  </div>
</div>