How to find a lost AirPods case without the AirPods?

You can find it with the find my app or you can log into iCloud.com and press on find my and the location of your AirPod case should appear their if you are unable to find the case you can buy a replacement AirPod case if you have AppleCare+ if you dont then you can buy a replacement case from Apple.com or the Apple Support App

If you have the case with find my enabled you can go to the find my to see if the case is shown there