I did a bit of running when on holiday in Ibiza. Bloody hot, so do it early or as the sun goes down. Beautiful island, hilly in north and east. Flat near the airport and salt flats. Saw quite a few hardcore cyclists while there. So depending on where you stat, I'd take your shoes.
Fine in which case I apologise. But I have seen a lot of people sign up to forums like this to chase details which help them construct a story beyond the offical public line. You have only posted on this topic, so I was suspicious.