Yubico has declared end-of-life for the YubiKey Validation Server (YK-VAL) and YubiKey Key Storage Module (YK-KSM). These have been moved to YubicoLabs as a reference architecture. See article, YK-VAL, YK-KSM and YubiHSM 1 End-of-Life.
If you don’t want to use YubiCloud, you can host one of these validation server(s) yourself.
Third party implementations can be discovered on GitHub for example.