How would I have ui-router go to an external link, such as google.com?

Angular-ui-router doesn’t support external URL, you need redirect the user using either $location.url() or $window.open()

I would suggest you to use $window.open('http://www.google.com', '_self') which will open URL on the same page.

Update

You can also customize ui-router by adding parameter external, it can be true/false.

  $stateProvider
  .state('external', {
       url: 'http://www.google.com',
       external: true
  })

Then configure $stateChangeStart in your state & handle redirection part there.

Run Block

myapp.run(function($rootScope, $window) {
  $rootScope.$on('$stateChangeStart',
    function(event, toState, toParams, fromState, fromParams) {
      if (toState.external) {
        event.preventDefault();
        $window.open(toState.url, '_self');
      }
    });
})

Sample Plunkr

Note: Open Plunkr in a new window in order to make it working, because google doesn’t get open in iFrame due to some security reason.