the 15th of August
Buongiorno,
you are right to be a bit concerned...even though by now in 2015 you can always find something open - normaly any place that will be open, will be open in the morning. And even if it is not a supermarket, many times the bars are open, and several will have a few of the basic neccessities (pasta, bread, water...) but don't expect a huge selection.
If you could have the place your staying prepare you a welcome basket and then plan on at least one meal out at a restaurant that day it would be nice, alleaviating the stress of having to find some place that is open.
Buon Viaggio e Buon Ferriagosto