I deleted /usr/local/bin on my Mac. Is there any way I can see what was installed there? I accidentally ran rm -rf /usr/local/bin.  Yes, I know, I'm an idiot.

Is there anything short of attempting to run every single application on my Mac to see what applications need to be reinstalled?
Most GUI Applications don't touch /usr/local/bin, so the Applications in your /Applications folder should still be in working condition. Some do install command line tools, but usually there is a menu item in the help or program menu to reinstall that command line item. Bottom line: If you don't use the command line much, you should be fine. If you use it frequently, you will see a "File not found" error when trying to run the command.

The only way to see what was in there, is indeed a backup.