In all cases where you create something and get a 201 back, the response will also include a Location HTTP header whose value is the URI to use in subsequent calls to reference this object. The same URI is also available as the "resources.self.ref" field in the returned JSON.
For people, the "id" part of a URI is the same as the value of the "id" field you get back. For content and place objects, it is not -- but you'll get the contentId or placeId field in the returned JSON to acquire those.
Craig, thank you very much for your quick and helpful reply. When writing my question, I hadn't realized/remembered that the 201 return body will include the JSON representation of the newly-created place.