To me, both are correct:
The date when the photo was taken, and the date the photo was taken. You can omit the "when" there, as well as you can omit the "why" in: "the reason (why) I told you this is..."
To me again, the only alternative would be "the date on which the..." and "the reason for which I ..."
This doesn't mean other versions can't be heard and perfectly understood.