You've placed "a fiatal orvos" just before the verb, so that's the element of the sentence that you are emphasizing. In that case, "a kórház mögött" should be placed after the verb.
But it changes the emphasis. This is sentence "a fiatal orvos zenél kórház mögött", is answer for "Ki" (who is painting behind the hospital) and
"a fiatal orvos kórház mögött zenél" is answer for
"Hol" ? (where is the boy painting?).