Not sure what's so bad about displaying the path in the log, but here are two other suggestions:
Click "File" in the main menu. The paths of the most recently opened programs are shown in the "Recently used file list," whose length you can set under Tools --> Options --> Preferences --> General.
Alternatively, select File --> Save As... from the menu. The "Save As" dialog window should show the folder in which the current program resides. In addition, the path is displayed in the status line of the main SAS window while the "Save As" dialog is open.