"Tengo una cita con él a mediodía."
I just checked - 'mediodía' is a masculine word...so I am still confused as to why 'al' is not accepted. If it was because it was feminine then it would say 'a la mediodía' but it just says 'a mediodía'.
In that case your answer is correct and should be accepted. File a request. (I just read a thread on word reference saying al mediodía is correct, not a mediodía