We can write the nested properties look like below code.
Go to live demo link http://embed.plnkr.co/CN8fO7/preview
 
Go to live demo link http://embed.plnkr.co/CN8fO7/preview
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 | <li ng-repeat="country in countries | filter: { locations: [{ cityId: search.locations.cityId }] }"> | 
<li ng-repeat="shop in shops | filter: { locations: [{ cityId: search.locations.cityId }] }">
The AngularJs Reference file is
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 | <script src="//ajax.googleapis.com/ajax/libs/angularjs/1.3.8/angular.min.js"></script> | 
<script src="//ajax.googleapis.com/ajax/libs/angularjs/1.3.8/angular.min.js"></script>The code-sample for HTML page
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 | <body ng-app="myApp">  <div ng-controller="ngController">    <input type="text" ng-model="Selected_CityId" />    <div ng-repeat="country in countries | filter : search">      Country : {{country.name}}       Locations : {{ country.locations }}    </div>  </div></body> | 
<body ng-app="myApp">
  <div ng-controller="ngController">
    <input type="text" ng-model="Selected_CityId" />
    <div ng-repeat="country in countries | filter : search">
      Country : {{country.name}} 
      Locations : {{ country.locations }}
    </div>
  </div>
</body>
The code-sample AngularJs
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 | var app = angular.module('myApp', []);app.controller('ngController', function($scope) {  $scope.countries = [{    "name": "USA",    "category_id": 1,    "locations": [{      "cityId": 22,      "regionId": 1    }]  }, {    "name": "India",    "category_id": 2,    "locations": [{      "cityId": 30,      "regionId": 2    }]  }];  $scope.search = function(shop) {    if ($scope.Selected_CityId === undefined || $scope.Selected_CityId.length === 0) {      return true;    }    var match = false;    angular.forEach(shop.locations, function(location) {      if (location.cityId === parseInt($scope.Selected_CityId)) {        match = true;      }    });    return match;  };}); | 
var app = angular.module('myApp', []);
app.controller('ngController', function($scope) {
  $scope.countries = [{
    "name": "USA",
    "category_id": 1,
    "locations": [{
      "cityId": 22,
      "regionId": 1
    }]
  }, {
    "name": "India",
    "category_id": 2,
    "locations": [{
      "cityId": 30,
      "regionId": 2
    }]
  }];
  $scope.search = function(shop) {
    if ($scope.Selected_CityId === undefined || $scope.Selected_CityId.length === 0) {
      return true;
    }
    var match = false;
    angular.forEach(shop.locations, function(location) {
      if (location.cityId === parseInt($scope.Selected_CityId)) {
        match = true;
      }
    });
    return match;
  };
});
The Full Example code-sample as given below
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 | <!doctype html><html lang="en"><head>  <meta charset="UTF-8">  <script src="//ajax.googleapis.com/ajax/libs/angularjs/1.3.8/angular.min.js"></script>  <script>    var app = angular.module('myApp', []);    app.controller('ngController', function($scope) {      $scope.countries = [{        "name": "USA",        "category_id": 1,        "locations": [{          "cityId": 22,          "regionId": 1        }]      }, {        "name": "India",        "category_id": 2,        "locations": [{          "cityId": 30,          "regionId": 2        }]      }];      $scope.search = function(shop) {        if ($scope.Selected_CityId === undefined || $scope.Selected_CityId.length === 0) {          return true;        }        var match = false;        angular.forEach(shop.locations, function(location) {          if (location.cityId === parseInt($scope.Selected_CityId)) {            match = true;          }        });        return match;      };    });  </script></head><body ng-app="myApp">  <div ng-controller="ngController">    <input type="text" ng-model="Selected_CityId" />    <div ng-repeat="country in countries | filter : search">      {{country.name}} {{ country.locations }}    </div>  </div></body></html> | 
<!doctype html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <title>filter nested properties in angularjs</title>
  <script src="//ajax.googleapis.com/ajax/libs/angularjs/1.3.8/angular.min.js"></script>
  <script>
    var app = angular.module('myApp', []);
    app.controller('ngController', function($scope) {
      $scope.countries = [{
        "name": "USA",
        "category_id": 1,
        "locations": [{
          "cityId": 22,
          "regionId": 1
        }]
      }, {
        "name": "India",
        "category_id": 2,
        "locations": [{
          "cityId": 30,
          "regionId": 2
        }]
      }];
      $scope.search = function(shop) {
        if ($scope.Selected_CityId === undefined || $scope.Selected_CityId.length === 0) {
          return true;
        }
        var match = false;
        angular.forEach(shop.locations, function(location) {
          if (location.cityId === parseInt($scope.Selected_CityId)) {
            match = true;
          }
        });
        return match;
      };
    });
  </script>
</head>
<body ng-app="myApp">
  <div ng-controller="ngController">
    <input type="text" ng-model="Selected_CityId" />
    <div ng-repeat="country in countries | filter : search">
      {{country.name}} {{ country.locations }}
    </div>
  </div>
</body>
</html>
Go to live demo code link http://embed.plnkr.co/CN8fO7/preview