This video shows the exact location of each Data Pad in the game, in order of missions.
(credits to WikiGameGuides for the video.)
I recommend watching the whole video, Each mission has 2 Data Pads, one obtainable on any difficulty and another obtainable only on Legendary difficulty.
Times for each Data Pad in the video:
Winter Contingency:
Data Pad 10: 00:00 Only Legendary difficulty
Data Pad 1 : 00:39 Any difficulty
Oni: Sword Base:
Data Pad 11: 01:15 Only Legendary difficulty
Data Pad 2 : 02:12 Any difficulty
NightFall:
Data Pad 3: 02:53 Any difficulty
Data Pad 12 : 03:02 Only Legendary difficulty
Tip of the Spear:
Data Pad 4: 04:12 Any difficulty
Data Pad 13 : 05:00 Only Legendary difficulty
Long Night of Solace:
Data Pad 5: 05:40 Any difficulty
Data Pad 14 : 05:56 Only Legendary difficulty
Exodus:
Data Pad 6: 06:27 Any difficulty
Data Pad 15 : 07:04 Only Legendary difficulty
New Alexandria:
Data Pad 16: 07:55 Only Legendary difficulty
Data Pad 7 : 08:30 Any difficulty
The Package:
Data Pad 8: 09:13 Any difficulty
Data Pad 17 : 09:35 Only Legendary difficulty
The Pillar of Autunumn:
Data Pad 18: 10:22 Only Legendary difficulty
Data Pad 9 : 10:43 Any difficulty
Lone Wolf:
Data Pad 19: 11:04 Only Legendary difficulty