Granny Rags has two side missions for you to complete in High Overseer Campbell, which have no bearing on your main objective in this mission. Completing both side missions will reward you with two Runes. She is located in the first area you come across, in the alley to the right. You'll see her throwing things off of a balcony, so go there and you'll find her downstairs.
Your first side mission for Granny Rags involves getting rid of three "gentlemen callers," which are three members of the Bottle Street Gang. They are standing outside of her front door, which makes it very hard to do it nonlethally. If you're doing it that way first, make sure to save, as it may take a few tries.
You can choke out the enemy on the left, if you approach from the right, and drag him backwards, hiding him by the archway. For the other two, you need to utilize your Sleep Darts, shooting the one on the right first and quickly hitting the one by the door next. When you have taken them out, whether nonlethally or in other ways, report back to Granny Rags to finish and get your Rune.
The second side mission involves infecting the distillery used by the Bottle Street Gang in making bootleg elixirs. Your first task is to get to Galvani's place, which is located past the first Wall of Light. To get the rat viscera easily from Galvani's place, get onto the topmost balcony outside and use the door to get inside. Once inside, go to the large bookshelf and grab the highlighted book, which will move the bookshelf and access a hidden room. Grab the rat viscera and then go back outside.
You need to go to the Dunwall Whiskey Distillery, which is in the alley across from Granny Rags' place. Once inside, you can find some wooden planks that form a ramp that lead up to some pipes and the roofs of the buildings. There are plenty of enemies in the way, including 2-3 by the entrance to the main building.
Once you get into the main building, go into the room on the right (requires Master Key, which you can get from guards or the room behind the partially closed metal door) and you will find some pipes that you can use to get higher ground. Blink onto the three parallel pipes, then look up and to the right to find another higher pipe along the wall. There is one guard walking along the entrance to the next area, so take care of him before moving on.
You're now in a room full of barrels, and there are some stairs leading down. Go down these stairs and turn around at the bottom to find a locked door (Master Key required to unlock it) and a small opening you can crawl through. Once you're in this room, go up to the barrel with the tap attached and press the <Action Button> to get a prompt to infect it. Once you do that, escape the same way that you entered and go back to Granny Rags to get another Rune.