Powershell script to iterate through folder and restore SQL backups
This is mostly style things, but:


You should store all your constants at the top (including $logsFolder)
#this ouputs the SQL output into a logfile: you misspelled outputs
You should use the string concatenation syntax:



"TO N'$($sqlDatabaseLocation)$($newDBName)_log.ldf',"




You only use $todayUK once, so you should include it directly as a string instead of declaring it.
Instead of concatenating each string component together, use a multi line string operator like @" or a trailing backtick `.



    [string] $dbCommand = @"RESTORE DATABASE [$newDBName]
FROM    DISK = N'$backupFilePath' 
WITH    FILE = 1,
MOVE N'$newDBName'
TO N'$($sqlDatabaseLocation)$($newDBName).mdf', 
MOVE N'$($newDBName)_log'
TO N'$($sqlDatabaseLocation)$($newDBName)_log.ldf',
NOUNLOAD, REPLACE, STATS = 5"




Now, you can just directly call that string instead of assigning it to $dbCommand:



    Write-Host @"RESTORE DATABASE [$newDBName]
FROM    DISK = N'$backupFilePath' 
WITH    FILE = 1,
MOVE N'$newDBName' #more stuff here