Once you finish The New Kid in Town, you will be able to explore South Park. In the top left corner of the map is Skeeter's Bar, so go there and head inside. Talk to Skeeter and he mentions there are rats in his basement, so he asks you to clear them for him.
Go down into the basement and you'll see four rats running around. Some of these you can take down via the environment, such as the teetering kegs, as well as the bottle you can break on the pool table. This bottle creates a pool of water and you can shoot the electric sign to electrocute that rat. Once you clear all of the rats, talk to Skeeter again to finish the quest, with him and the Bartender becoming your friends.
