Both Eroski supermarkets in Santa Eulalia (there is a new one on the Es Cana road that opened this winter) are open on Sundays from ten in the morning until mediodía which in Ibiza speak is 2pm - don't ask me why. Alternatively if you have a car there are two fruit & veg shops on the Santa Eulalia-Ibiza road that are open until around eight in the evening where you can buy milk, bread, cheese, wine etc.. and of course fruit & veg.
errrr not quite as straight forward as that.......practically every one who i encounter using the word mediodia is talking about the middle of the day rather than a specific time. a bit like the way you might say lunchtime.
when they're talking about 12 noon, without fail people say "doce de la mañana" and never mediodia.