The easiest way to save an image is click-and-drag it from Safari to the desktop.
To save the URL from Safari, hold down the "control" key and click on the image. (Or, if you have a two-button mouse, right-click on the image.) In the popup menu, choose "Open Image in New Window".
Then, from the new window, you can drag the web site icon (often a globe) to your desktop to save the URL - or you can bookmark it.
You can do that, but it's still an incredibly clunky workaround that comes nowhere close to matching the functionality that existed in OS 9 and earlier, when simply dragging the graphic to the desktop (or downloading most any file in any way) automatically caused the orignating URL to be put in the Get Info box.