$(document).ready(function(){
$('#pkdateselect2').daterangepicker({
"singleDatePicker": true,
"startDate": "2018-02-01",
"minDate" : "2018-02-01"
},
  function(start, end, label) {
  $.post("ajax/pkaction.php",
        {action: "checkdate",
         client_id: "<?php echo $id; ?>",
         userid: "<?php echo $userid; ?>",
         pkdateselect: start.format('YYYY-MM-DD')
         },
        function(data){
            $('#pkdateselect2').html(data.wybranadata);
            $('#wyborgodzin').removeClass('invisible');
            $('#pksave').removeClass('invisible');
            $('#godziny').html(data.godziny);

        }
        , "json"
    );

   });
});

<input type="text" id="pkdateselect2" class="form-control" name="pkdateselect2">

<select class="form-control" id="godziny" name="godziny">
<option value="08:00:00">08:00</option>
<option value="08:15:00">08:15</option>
</select>

<button type="submit" id="pksave" class="btn btn-primary invisible">Zapisz</button>

$(document).ready(function(){
$('#pksave').click(function(){
    console.log('value ' + $("godziny").val());
    $.post("ajax/pkaction.php",
        {action: "pksave",
         client_id: "<?php echo $id; ?>",
         userid: "<?php echo $userid; ?>",
         pkdateselect2: $("#pkdateselect2").val(),
         godziny: $("godziny").val()  },
        function(data){

            $('#pkmodalbody').html(data.results);

        }
        , "json"
    );
});
});

$("godziny").val()

$("#godziny").val()