Downloading and installing the vSphere Client 6.0 involves obtaining the legacy C# application used for managing older ESXi hosts. Since VMware has transitioned to web-based management, version 6.0 is considered legacy software. 1. Locate the Download Source
Here’s a direct, practical answer:
The (the desktop C# client, not the web client) is officially available from Broadcom (which now owns VMware). vsphere client 60 download high quality