The following piece of code determines and returns the node which a specified user is logged into.

How to use:

1. Replace variable username by the user ID
2. Execute as background script / fix script

(function () {
  var username = 'admin'; //sys_user.user_name

  var userSession = new GlideRecord('v_user_session');
  userSession.addQuery('user', username);
  userSession.addActiveQuery();
  userSession.setLimit(1);
  userSession.query();

  if (!userSession.next()) {
    gs.log('User is not logged in');
    return;
  }

  var sessionID = userSession.getValue('session_id');

  var transactionLog = new GlideRecord('syslog_transaction');
  transactionLog.addQuery('session', sessionID);
  transactionLog.orderBy('sys_created_on');
  transactionLog.setLimit(1);
  transactionLog.query();

  if (!transactionLog.next()) {
    gs.log('Unknown error');
    return;
  }

  var systemId = transactionLog.getValue('system_id'); 
  systemId = systemId.split(':');
  var node = systemId[systemId.length - 1];

  gs.log(username + " is logged into node: " + node);
})();

Disclaimer: Please, always test the script in non-productive environments before running in a productive instance. Script was reviewed at the creation time but may break/get unexpected results due to instance versioning and SN API upgrades.