You could possibly make multiple sub-directories to hold different sort of images in your applications. The parent directory could be something like this,
https://192.168.1.1/Images, then inside it you can create different folders for EmployeePhotos, ApplicationImages (such as the logo, social buttons etc). Do not create the folder MyWebService; clients know that the IP address targets your own service.
You can possibly use the Server.MapPath() function, if you're going to work around in the absolute paths. MapPath returns the absolute paths. Since you do not want yourself getting hands dirty, or to allow anyone else to use that absolute path to the directory, you can ignore it. :)
In .NET, you can possibly enumerate over multiple directories, and use which so ever directory over the machine that you like. A code to get directories from machine in .NET is like this,
Environment.GetSpecialFolder(Environment.SpecialFolder.ApplicationData);
You can read
this MSDN document[
^], to learn more on this process.
That won't be a good idea, you can store the images right inside a local "Images" folder, that would indicate that inside your web service this folder is meant for the image data only.