The CORS headers are not set for Places API web service on Google backend servers. So you won’t be able to call Places API web service from the client side JavaScript code due to the Same-Origin policy of the browsers.
In order to use Places on client side JavaScript you have to use a Places library of Google Maps JavaScript API. The places library has nearby, radar and text search functionality very similar to the corresponding web service.
For further details please have a look at the documentation:
https://developers.google.com/maps/documentation/javascript/places
Hope it helps!