You can combine Get-CimInstance with Get-LocalUser:

$userName = 'other.user'
(
  Get-CimInstance Win32_UserProfile -Filter "SID = '$((Get-LocalUser $userName).Sid)'"
).LocalPath

This outputs the path of the targeted user's profile directory, such as C:\Users\other.user.

Note: The profile directory is typically, but not necessarily the same as a user's home directory - the latter can be configured to point elsewhere, such as to a network share, and is reflected in a pair of environment variables for the current user, HOMEDRIVE and HOMEPATH.

To get the true home directory:

• If the targeted user is stored in Active Directory, the following may work (untested):

  $userName = 'other.user'
  $user = Get-ADUser $userName -Property HomeDrive, HomeDirectory
  '{0}{1}' -f $user.HomeDrive, $user.HomeDirectory
  

• For a local-only user:

  • I'm personally not aware of a method, given that the HOMEDRIVE and HOMEPATH environment variables are dynamically added to the registry, when that user logs on to a window station (creates an OS session), under HKEY_CURRENT_USER\Volatile Environment. By contrast, if you load another user's profile file (the hidden NTUSER.DAT file located in the user's profile directory) into the registry on demand, such as via reg.exe load or via the CreateProcessWithLogon() WinAPI function (as also used by runas.exe^[1]), these values are not added.

  • If someone knows if and where the home-directory information is contained in the non-volatile information of a user's profile (as accessible via the registry after loading it), do let us know.

As for what you tried:

The relevant properties of the System.DirectoryServices.DirectoryEntry (whose type accelerator is [adsi]) instance should be .Profile and .HomeDirDrive / .HomeDirectory, but at least on my Windows 10 machine they aren't populated; e.g.:

PS> ([adsi] 'WinNT://localhost/jdoe,user') | Format-List *

# ...
HomeDirectory              : {}
# ...
Profile                    : {}
HomeDirDrive               : {}
# ...

^{[1] Beware that something like runas.exe /profile /user:$userName cmd /c echo %HOMEDRIVE%HOMEPATH% in effect reports %HOMEDRIVE% as C: and %HOMEPATH% as \Windows\System32(!), based on the behavior of CreateProcessWithLogon(), which - strangely - sets these variables to the working directory of the launched process, which defaults to C:\Windows\System32.}

I think because the HomeDirectory attribute is not in the default output set from Get-ADUser, you need to add it to the required Properties aswell.
This may be part of a larger script, but from the question I fail to see why you would need this:

$DirectoryInfo = Get-Item \\Fileserver\Users
$strFilter = $DirectoryInfo.FullName + '\*'

since you already have the UNC path for the users home directories.

I cannot test this right now, but you could try like this:

$strFilter = '\\Fileserver\Users\*'
$AdUser = Get-AdUser -Filter "HomeDirectory -like $strFilter" -Properties HomeDirectory
$AdUser

or use a Where-Object to get what you want:

$strFilter = '\\Fileserver\Users\*'
$AdUser = Get-AdUser -Filter * -Properties HomeDirectory | Where-Object { $_.HomeDirectory -like $strFilter }
$AdUser

*         \2A
(         \28
)         \29
\         \5C
NUL       \00

You do this by prepending a backslash \ to each of these characters and replacing the characters themselves by their ASCII code in hex. The ( becomes \28, the backslash \ becomes \5c etc.

This uses a small function to escape these characters for a LDAP search filter:

function Escape-LdapSearchFilter([string] $Filter) {
    return $Filter -creplace '\*', '\2a' `
                   -creplace '\(', '\28' `
                   -creplace '\)', '\29' `
                   -creplace '/' , '\2f' `
                   -creplace '`0', '\00' `
                   -creplace '\\(?![0-9A-Fa-f]{2})', '\5c'
}

$strFilter = Escape-LdapSearchFilter "\\Fileserver\Users\"
# for LDAP you must use the correct attribute name, so `homeDirectory` with a lower-case `h`
$AdUser = Get-AdUser -LDAPFilter "(homeDirectory=$strFilter*)" -Properties HomeDirectory
$AdUser

You're looking for the Set-ADUser cmdlet. It has a -HomeDirectory parameter, which obviously allows you to set the user's home directory, and an -Identity parameter that specifies which user you are editing. It also has a -HomeDrive parameter that specifies the drive letter for their home directory.

# 1. Get the user, based on their "display name"
$User = Get-ADUser -LDAPFilter '(&(displayname=Trevor Sullivan))';
# 2. Change the user's home directory and home drive
Set-ADUser -Identity $User.SamAccountName -HomeDirectory \\fileserver\users\trevor -HomeDrive U;

Given the following CSV file contents:

The following script should set the home drives:

# 1. Import the user data from CSV
$UserList = Import-Csv -Path c:\test\Users.csv;

# 2. For each user ...
foreach ($User in $UserList) {
    # 2a. Get the user's AD account
    $Account = Get-ADUser -LDAPFilter ('(&(displayname={0}))' -f $User.DisplayName);
    # 2b. Dynamically declare their home directory path in a String
    $HomeDirectory = '\\fileserver\users\{0}' -f $Account.SamAccountName;
    # 2c. Set their home directory and home drive letter in Active Directory
    Set-ADUser -Identity $Account.SamAccountName -HomeDirectory $HomeDirectory -HomeDrive u;
}

Use -Properties HomeDirectory at the tail end of your get-adusers cmdlet:

get-aduser -searchbase "%OUpath" -filter {homedirectory -like '\\venus*'} -Properties HomeDirectory

That should do it!

Microsoft has updated their Active Directory powershell module and it is included with RSAT. Should you not want to use a third-party's modules, the following lists the sAMAaccountName and homeDirectory attributes for all users in the "JustAnOrgUnit" OU -- pretty much the same as @nimizen's answer, just without the Quest requirement.

Import-Module ActiveDirectory
Get-ADUser -SearchBase "OU=JustAnOrgUnit,DC=example,DC=com" -Filter * -Property * |
    Select-Object -Property sAMAccountName,homeDirectory |
        Export-CSV -Path C:\somefile.csv