How do I validate user input in a loop?

Your script is almost fine, you're just having some trouble with your if condition:

$UserInput -lt 1 -gt 11 -ne 'q'

This is how PowerShell is evaluating the statement, and why it is always entering the if condition. Using the word test as $userInput:

'test' -lt 1   # => $false
$false -gt 11  # => $false
$false -ne 'q' # => $true

This is how it should look, note the use of -and:

'test' -lt 1 -and 'test' -gt 11 -and 'test' -ne 'q'

There is an alternative you can use with the -notmatch operator which allows the use of Regular Expressions.

In the example below, $UserInput -notmatch $regex will return $true at any user input that is not the ones we see on the $validoptions array (from 1 to 11 + q).

$validoptions = 1..11 + 'q'
$regex = '^{0}$' -f ($validoptions -join '$|^')
# Regex: ^1$|^2$|^3$|^4$|^5$|^6$|^7$|^8$|^9$|^10$|^11$|^q$

$waitForUSer = {
    'Press ENTER to Continue...'
    Read-Host
}

do
{
    sysInfoMenu
    $UserInput = Read-Host "Please select an option from the menu"
    
    if ($UserInput -notmatch $regex){
        Write-Warning "Invalid input, please select an option from the menu"
        & $waitForUSer
        continue # => Go to Until, skip next lines
    }

    if($UserInput -eq 'q'){
        continue # => Go to Until and end the loop
    }
   
    $info = switch ($UserInput)
    {
      '1'  { 'Option 1' }
      '2'  { 'Option 2' }
      '3'  { 'Option 3' }
      '4'  { 'Option 4' }
      '5'  { 'Option 5' }
      '6'  { 'Option 6' }
      '7'  { 'Option 7' }
      '8'  { 'Option 8' }
      '9'  { 'Option 9' }
      '10' { 'Option 10' }
      '11' { 'Option 11' }
    }
      
    $info # => Show selection
    & $waitForUSer
}
until ($UserInput -eq 'q')

You have a couple of structural problems.

• You didn't terminate your function.
• You didn't call your function.
• You keep calling Get-ComputerInfo which is slow and only needs to be done once.
• Your menu needs to be in your loop so you can clear the screen and get rid of the previous answers and/or error messages.

Here's some alternative code which I've commented to help you learn.

function SysInfoMenu {

    param (
     [Parameter(Mandatory=$False)]
      [string] $Title = 'System Information'
    )

#Setup:

   $ByeBye   = $False           #Set initial value.
   #Hide the Progress Bar. Remove line if not wanted.
   $ProgressPreference = "SilentlyContinue"
   $CompInfo = Get-ComputerInfo #You only need to call once.

#Main Function Code:

do {
    Clear-Host

    Write-Host "=============== $Title ==============="
    "`n`n"
    Write-Host "Please select from the following options:"
    "`n"
    Write-Host "Press  1 for: OS System"
    Write-Host "Press  2 for: OS Type"
    Write-Host "Press  3 for: OS Architecture (32 or 64 bit)"
    Write-Host "Press  4 for: OS Version"
    Write-Host "Press  5 for: OS Bios Version"
    Write-Host "Press  6 for: Computer Brand"
    Write-Host "Press  7 for: Computer Name"
    Write-Host "Press  8 for: Current Domain"
    Write-Host "Press  9 for: Computer Model"
    Write-Host "Press 10 for: Current User"
    Write-Host "Press 11 for: Timezone"
    Write-Host "Press 'q' to quit."

    $UserInput = Read-Host "Please select an option from the menu"
        
 #Note: use of Break to leave switch once match is found.
       
    switch ($UserInput) {
       '1' {$CompInfo.OSName         ;Break}
       '2' {$CompInfo.OSType         ;Break}
       '3' {$CompInfo.OSArchitecture ;Break}
       '4' {$CompInfo.OSVersion      ;Break}
       '5' {$CompInfo.BiosVersion    ;Break}
       '6' {$CompInfo.CsManufacturer ;Break}
       '7' {$CompInfo.CsName         ;Break}
       '8' {$CompInfo.CsDomain       ;Break}
       '9' {$CompInfo.CsModel        ;Break}
      '10' {$CompInfo.CsUserName     ;Break}
      '11' {$CompInfo.TimeZone       ;Break}
      'q'  {$ByeBye = $True          ;Break}
      default {"Invalid input, please select an option from the menu"}
    } #End Switch      
          
    if (-not $ByeBye) { pause }
        
  } until ($ByeBye) #Exit via $ByeBye value!

} #End Function SysInfoMenu

SysInfoMenu #Call your function