Try a hard_code ... having DayofMon > 15 ... I'm more of an Oracle guy, so from my experience there you can't put a Windowed function in the result of Having.

Try this: use max function on select.

SELECT 
    [OrganisationID] 
    ,[MailboxLocationName] AS Location 
    ,MailboxCode as LocationCode 
    ,Max(DayofMon) as [DayofMon]
    ,COUNT(DISTINCT [UPN]) AS [Count]
FROM 
    [ExchangeUserMailbox]
GROUP BY 
    [OrganisationID], [MailboxLocationName], MailboxCode

The HAVING clause is designed for for filtering by aggregated calculations, hence it is performed AFTER the GROUP BY is complete so it can access the aggregated values. What you need requires filtering BEFORE grouping is performed, so the having clause isn't helpful.

You could just filter the data where DayOfMon is in (28, 29, 30 or 31)

SELECT
        OrganisationID
      , MailboxLocationName AS Location
      , MailboxCode         AS LocationCode
      , 30                  AS DayofMon 
      , COUNT(DISTINCT UPN) AS [Count]
FROM [ExchangeUserMailbox]
WHERE DayofMon IN (28,29,30,31)
GROUP BY
        OrganisationID
      , MailboxLocationName
      , MailboxCode

or you could make use of ROW_NUMBER() like this:

SELECT
        OrganisationID
      , Location
      , LocationCode
      , 30                  AS DayofMon 
      , COUNT(DISTINCT UPN) AS [Count]
FROM (
        SELECT
                OrganisationID
              , MailboxLocationName   AS Location
              , MailboxCode           AS LocationCode
              , UPN
              , ROW_NUMBER() OVER (PARTITION BY OrganisationID
                                                , MailboxLocationName
                                                , MailboxCode
                                   ORDER BY DayofMon DESC) AS rn
        FROM [ExchangeUserMailbox]
        ) AS d
WHERE d.rn = 1
GROUP BY
        OrganisationID
      , Location
      , LocationCode
;

Which will give the number 1 to each row having the largest DayOfMon for each "partition"

The most straightforward way is using a subquery:

SELECT 
    eum.[OrganisationID] 
    ,eum.[MailboxLocationName] AS Location 
    ,eum.MailboxCode as LocationCode 
    ,eum.DayofMon 
    ,COUNT(DISTINCT [eum.UPN]) AS [Count]
FROM 
    [ExchangeUserMailbox] AS eum
WHERE eum.DayofMon =
      (SELECT MAX(eum2.DayofMon)
       FROM   [ExchangeUserMailbox] AS eum2
       WHERE  eum2.[OrganisationID] = eum.[OrganisationID]
       AND    eum2.[MailboxLocationName] = eum.[MailboxLocationName]
       AND    eum2.MailboxCode = eum.MailboxCode
      )
GROUP BY 
    eum.[OrganisationID], eum.[MailboxLocationName], eum.DayofMon, eum.MailboxCode

The "hard coded" solutions work, but are more brittle. This way, you are sure to always get the records with the highest DayofMon value (even if it is an unexpected value) and you get the actual value of DayofMon instead of a hard coded value.