This was pretty much on the money. I had to treat the \ a little differently as it wouldn't insert with single or double quotes. Using $backslash and declaring it did the trick.

Now I need to work on a script to verify the names in the text file and to verify that there is a home folder present and that there are no blank lines in the file before it is processed.

I had to copy off over 500 folders with this today and it worked like a charm. Thanks again!

$inFile = read-host "Please enter the complete path and file name to be used" 

$outdest = read-host "Please enter the detination path" 

$names = Get-Content $inFile

$backslash = "\"

foreach($name in $names)
{
[array]$list += Get-ADUser -Filter {(City -like "Fort someplace" -and Name -like $name)} -Property SamAccountName,HomeDirectory
}

for ($i=0; $i -lt $($list.Length); $i++)
{

    $source = $list[$i].HomeDirectory
    $SamAccountName = $list[$i].SamAccountName
    $dest= "$outdest$backslash$SamAccountName"
    $what = @("/COPYALL","/B","/SEC","/MIR")
    $options = @("/R:0","/W:0","/NFL","/NDL","/MT:50")
    $cmdArgs = @("$source","$dest",$what,$options)
    robocopy @cmdArgs
}