Using Ajax to get and show mysqli query results - php

Question

I'm practicing Ajax by making an app that checks the content of a database table and inserts it into my page asynchronously, only the first row of the table is printing and I'm not sure why. This is my code:
index.php - Here is where I create the page with an empty space in #result_table that should get filled by the table fetched by places.php
<div class="row">
<div class="col-xs-3">
<button type="button" class="btn btn-lg btn-default" id="showPlaces" name="showPlaces">Mesas</button>
</div>
</div>
<div class="row">
<div class="col-lg-12">
<table class="table table-striped">
<thead>
<tr>
<th>Nombre</th><th>Piso</th><th>Cliente</th><th>Mesero</th><th>Area</th><th>Estado</th>
</tr>
</thead>
<tbody id="result_table">
</tbody>
</table>
</div>
</div>
places.php - Here I make the query and return(?) the data
<?php
include("con.php");
mysqli_select_db("unicentaopos", $c);
$result = mysqli_query($c,"SELECT * FROM places");
while ($places = mysqli_fetch_array($result)) {
echo "<tr>";
echo "<td>". $places ['NAME']."</td>";
echo "<td>". $places ['FLOOR']."</td>";
echo "<td>". $places ['CUSTOMER']."</td>";
if (!$places['WAITER']) {
echo "<td>" . "VACIO" . "</td>";
} else {
echo "<td>". $places ['WAITER']."</td>";
}
echo "<td>". $places ['AREA']."</td>";
echo "<td>". $places ['ESTADO']."</td>";
echo "</tr>";
}
mysqli_free_result($result);
?>
script.js - Here I use jQuery to make the Http request
$( document ).ready(function() {
$('#showPlaces').click(function(){
$.ajax({
type:'GET',
url: 'places.php',
dataType: 'html',
success: function(result){
$('#result_table').html(result);
} // End of success function of ajax form
}); // End of ajax call
});
});
con.php - Here I connect to the database
<?php
$c = mysqli_connect("localhost","root","root","unicentaopos");// Check connection
if (mysqli_connect_errno()) { // Si hay error lo menciona en alerta.
echo '<div class="alert alert-danger">';
echo 'Failed to connect to MySQL: ' . mysqli_connect_error();
echo '</div>';
} else { // Si no hay error.
}
?>
I've been stuck on this for a while, could you guys help me pinpoint the problem? I guess it's either the way i'm returning the data from places.php, or I'm making a mistake in the connection, wich would be weird since that very same code worked for a simple example I did a while ago.
Please remember, I'm new to Ajax so anything you can tell me that helps me improve will be very welcome.
Fixed it with help of the comments and edited the post with the working code.