How to retrieve user’s current city name?

As of iOS 5 MKReverseGeoCoder is Deprecated!

So you want to use CLGeocoder with CLLocationManager, very simple and works with block.

Example:

- (void)locationManager:(CLLocationManager *)manager
    didUpdateToLocation:(CLLocation *)newLocation
           fromLocation:(CLLocation *)oldLocation
{
   [self.locationManager stopUpdatingLocation];

   CLGeocoder * geoCoder = [[CLGeocoder alloc] init];
    [geoCoder reverseGeocodeLocation:newLocation
                   completionHandler:^(NSArray *placemarks, NSError *error) {
                       for (CLPlacemark *placemark in placemarks) {
                           .... = [placemark locality];
                       }
                   }];
}

Edit: Instead of a for in loop you can also do:

NSString *locString = placemarks.count ? [placemarks.firstObject locality] : @"Not Found";