I can search for websites using:
Get-WmiObject -Namespace \"root\\WebAdministration\" -Class Site -Authentication PacketPrivacy -ComputerName $servers
Here's another option if you do not want to use the IIS:\ path.
$site = Get-IISSite -Name 'my-site' $appPool = Get-IISAppPool -Name $site.Applications[0].ApplicationPoolName