Formatting date/time values using the user's timezone in Apps Script.

Code.js

/**
 * @file A sample showing how to format date/time values in Apps Script so that they appear in the 
 * user's timezone. View a working version here: 
 * https://docs.google.com/spreadsheets/d/1VlI8HibL9kh_wlmO0G1ltMGVo6S-urGrDqDbfEp9eeY/edit
*/

/**
 * Add menu item after the spreadsheet opens.
 */
function onOpen() {
  SpreadsheetApp.getUi().createMenu('Sample')
      .addItem('Show sidebar', 'showSidebar')
      .addToUi();
}

/**
 * Show the sidebar.
 */
function showSidebar() {
  var page = HtmlService.createHtmlOutputFromFile('Page').setTitle('User Timezone Sample');
  SpreadsheetApp.getUi().showSidebar(page);
}

/**
 * Gets the timezone stored for the user.
 * @returns {string} The timezone of the user or null if not set.
 */
function getUserTimezone() {
  return PropertiesService.getUserProperties().getProperty('timezone');
}

/**
 * Sets a timezone for the user.
 * @param {string} timezone The timezone of the user.
 */
function setUserTimezone(timezone) {
  PropertiesService.getUserProperties().setProperty('timezone', timezone);
}

/**
 * Sets the timezone for the user, based on a timezone offset value.
 * @param {number} timezoneOffset The timezone offset of the user, as the difference in minutes 
 *                                between UTC and local time.
 * @see https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Date/getTimezoneOffset
 */
function setUserTimezoneFromOffset(timezoneOffset) {
  var timezoneOffsetMillis = Number(timezoneOffset) * 60 * 1000;
  var timezoneOffsetFormatted = Utilities.formatDate(new Date(Math.abs(timezoneOffsetMillis)), 
      'GMT', 'hh:mm');
  var timezoneOffsetSign = timezoneOffset > 0 ? '-' : '+';
  var timezone = 'GMT' +  timezoneOffsetSign + timezoneOffsetFormatted;
  setUserTimezone(timezone);
}

/**
 * Formats a date using the user's timezone. Throws an exception if no timezone has been set 
 * for the user.
 * @param {Date} date The date to format.
 * @param {string} format The date format to use.
 * @returns {string} The formatted date.
 */
function formatDateForUser(date, format) {
  var timezone = getUserTimezone();
  if (!timezone) {
    throw 'Error: Timezone not set.';
  }
  return Utilities.formatDate(date, timezone, format)
}

/**
 * Gets the current time as a string.
 * @return {string} The current time.
 */
function getCurrentTimeAsString() {
  return formatDateForUser(new Date(), 'yyyy-MM-dd hh:mm:ss a');
}

Page.html

<link rel="stylesheet" href="https://ssl.gstatic.com/docs/script/css/add-ons.css">

<div class="sidebar">
  <button id="show">Get current time from server</button>
  <pre id="time"></pre>
</div>

<script src="//ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
<script>
  $(function() {
    // Set the timezone offset every time the sidebar loads.
    google.script.run.setUserTimezoneFromOffset(new Date().getTimezoneOffset());
    
    // Setup the button handler.
    $('#show').bind('click', function() {
      google.script.run.withSuccessHandler(function(time) {
        $('#time').text('Time: ' + time);
      }).getCurrentTimeAsString();
    });
  });
</script>