The combination is 935. This guide explains how to open the safe without that knowledge and how to complete the Return to the Tower mission non-lethally.
There is a visual version of this guide at the end of this post.
There is also a secret room in the Dunwall Tower, here is to guide to find it: The Empress’ Secret Room in Dunwall Tower (Finding the Bone Charm inside the Dunwall Tower)
The Regent’s safe is actually tied to the nonlethal completion of the Return to the Tower mission. To get the key combination talk to the propaganda officer in the radio tower, which is to the right of the main entrance (you have to go up a lot of stairs). As soon as you get near him he will tell you the number combination for the Lord Regent’s Safe.
Go to the Lord Regent’s Bedchamber and open the safe. There is some loot in there, a note and the audiolog. Take the audiolog and go back up to where you found the propaganda officer and play it in the Broadcasting Device: