What is the fastest way to retrieve log files from an ESXi host? In my opinion, the best way is to configure remote logging via syslog server but this requires host reboot to apply configuration changes (KB1016621). The alternative method is to forward log files to different datastore.
If you don't have prepared syslog server for remote logging you can use vsphere client and generate system log bundles for particular host. But this takes some time.
The last method is I think the fastest one because it will allow you to access log files directly with your web browser. You can use web interface of the ESXi host, enter the following URL: https://ESXi_HOST_ADDR/host
The output should looks like shown at this picture:
You can download ESXi log files messages, hostd.log and vpxa.log now.