I am not able to place markers on the places which is already marked by google with other symbols .

Question

The info window and marker is not shown for the places which is already marked by google. for example: if you run the code and click anywhere , a marker and a info window will a

Answer 1

Hide those POIs:

styles: [{
    featureType: "poi",
    elementType: "labels",
    stylers: [{
        visibility: "off"
    }]
}]

working code snippet:

var map;
var myCenter = new google.maps.LatLng(51.508742, -0.120850);

function initialize() {
  var mapProp = {
    center: myCenter,
    zoom: 14,
    mapTypeId: google.maps.MapTypeId.ROADMAP,
    styles: [{
      featureType: "poi",
      elementType: "labels",
      stylers: [{
        visibility: "off"
      }]
    }]
  };

  map = new google.maps.Map(document.getElementById("googleMap"), mapProp);

  google.maps.event.addListener(map, 'click', function(event) {
    placeMarker(event.latLng);
  });
}

function placeMarker(location) {
  var marker = new google.maps.Marker({
    position: location,
    map: map,
  });
  var infowindow = new google.maps.InfoWindow({
    content: 'Latitude: ' + location.lat() + ' Longitude: ' + location.lng()
  });
  infowindow.open(map, marker);
}

google.maps.event.addDomListener(window, 'load', initialize);

html,
body,
#googleMap {
  height: 100%;
  width: 100%;
  margin: 0px;
  padding: 0px
}

<script src="http://maps.google.com/maps/api/js"></script>
<div id="googleMap"></div>

Answer 2

When you click on such a place(POI) there will no click be triggered on the map.

When you don't want to hide the POI's, you must trigger the click on your own.

Possible approach(see: How to get a click event when a user clicks a (business) place on the map )

//keep a reference to the original setPosition-function
var fx = google.maps.InfoWindow.prototype.setPosition;

//override the built-in setPosition-method
google.maps.InfoWindow.prototype.setPosition = function () {

  //this property isn't documented, but as it seems
  //it's only defined for InfoWindows opened on POI's
  if (this.logAsInternal) {
    google.maps.event.addListenerOnce(this, 'map_changed',function () {
      var map = this.getMap();
      //the infoWindow will be opened, usually after a click on a POI
      if (map) {
        //trigger the click
        google.maps.event.trigger(map, 'click', {latLng: this.getPosition()});
        //hide the default-infoWindow of the POI
        this.setMap(null);
      }
    });
  }
    //call the original setPosition-method
  fx.apply(this, arguments);
};

Demo: http://jsfiddle.net/doktormolle/1yrpm98q/