Edit in JSFiddle

(function(angular) {
  'use strict';

  var app = angular.module('MyApp', []);

  app.factory('GeolocationSvc', [
    '$q', '$window',
    function($q, $window) {
      return function() {
        var deferred = $q.defer();

        if(!$window.navigator) {
          deferred.reject(new Error('Geolocation is not supported'));
        } else {
          $window.navigator.geolocation.getCurrentPosition(function(position) {
            deferred.resolve({
              lat: position.coords.latitude,
              lng: position.coords.longitude
            });
          }, deferred.reject);
        }

        return deferred.promise;
      };
  }]);

  app.factory('ZipCodeLookupSvc', [
    '$q', '$http', 'GeolocationSvc',
    function($q, $http, GeolocationSvc) {
      var MAPS_ENDPOINT = 'http://maps.google.com/maps/api/geocode/json?latlng={POSITION}&sensor=false';

      return {
        urlForLatLng: function(lat, lng) {
          return MAPS_ENDPOINT.replace('{POSITION}', lat + ',' + lng);
        },

        lookupByLatLng: function(lat, lng) {
          var deferred = $q.defer();
          var url = this.urlForLatLng(lat, lng);

          $http.get(url).success(function(response) {
            // hacky
            var zipCode;
            angular.forEach(response.results, function(result) {
              if(result.types[0] === 'postal_code') {
                zipCode = result.address_components[0].short_name;
              }
            });
            deferred.resolve(zipCode);
          }).error(deferred.reject);

          return deferred.promise;
        },

        lookup: function() {
          var deferred = $q.defer();
          var self = this;

          GeolocationSvc().then(function(position) {
            deferred.resolve(self.lookupByLatLng(position.lat, position.lng));
          }, deferred.reject);

          return deferred.promise;
        }
      };
    }
  ]);

  app.controller('MainCtrl', ['$scope', 'ZipCodeLookupSvc',
    function($scope, ZipCodeLookupSvc) {
      $scope.zipCode = null;
      $scope.message = 'Finding zip code...';

      ZipCodeLookupSvc.lookup().then(function(zipCode) {
        $scope.zipCode = zipCode;
      }, function(err) {
        $scope.message = err;
      });
  }]);

})(angular);

<div ng-app="MyApp">
    <div ng-controller="MainCtrl">
      <div ng-show="zipCode">        
        <p>{{ zipCode }}</p>
      </div>
      <div ng-hide="zipCode">
        <p>{{ message }}</p>
      </div>
    </div>
</div>