You need to specify which ReST API you want to use. There is the "legacy" or internal ReST API that Alfresco primarily uses to support Share, and which should not be relied upon for 3rd-party integrations. The base URL for this would be
<yourProtocol>://<yourHost>:<exposedPort>/alfresco/service/... (HTTP BASIC)
<yourProtocol>://<yourHost>:<exposedPort>/alfresco/s/... (alias for service)
<yourProtocol>://<yourHost>:<exposedPort>/alfresco/wcservice/... (SSO as configured in Alfresco)
<yourProtocol>://<yourHost>:<exposedPort>/alfresco/wcs/... (alias for wcservice)
Of course yourProtocol, yourHost and yourPort depends on your specific infrastructure / setup. Even the /alfresco part may be changed, but in my experience rarely isn't. If you don't know how you can access your Alfresco system, you should talk with your Alfresco / system administrator.
The ReST v1 API - which is the recommended API to use since Alfresco 5.2 - can be accessed under
For the v1 ReST API, the API version is of course "1".
What you remarked as having found the endpoints /org/alfresco/repository/... refers to the source files of the web scripts, which implement the "legacy" / internal ReST API.