From the episode, Kirk doesn't go into detail as to what exactly was damaged and what efforts were made to repair them. The damage could have been external AND internal. We are only given information after the fact, that the result was "considerable" damage and Kirk orders a non-scheduled layover at a Starbase. It would be unusual for the crew not to attempt some repairs while en-route to the Starbase, IMO.
Robert Comsol wrote:
From the context of the episode and the naval analogy presented in this episode (e.g. "ashore" for "down on the planet") I understood that the ion storm mostly caused external "considerable damage" that requires "full repairs" and "a couple of days". I would also wonder why Kirk files a log entry at the beginning of the episode and fails to mention any repair effort by the crew. It's not his style to ignore accomplishments by his crew (compare log entries in "Where No Man Has Gone Before").