Continuity mistake: When Pacey is nursing his black eye with a raw steak, Joey comes into Doug's apartment to talk to Pacey. Just when Pacey says, "Looking out for ya," there is a frontal shot of Joey. Her hair is bunched up considerably in the back, near her right ear. As Pacey says, "To look after said girl," the next shot of Joey shows the bunched up hair in the back suddenly gone, and her hair is smooth.
Continuity mistake: At the end of the episode, Joey and Pacey are repainting over the ruined mural with light blue paint. Joey starts to paint a small section of the wall with her roller. Dawson then comes out of a room, and glances down the hallway to see them both painting. But Joey's patch of light blue paint at this point is suddenly much larger. It doesn't seem realistic that Joey would have been able to paint that much more of the wall, in the short amount of time elapsed.
Answer: It's the same apartment Joey had in NYC. Comparing it to the beginning of the Finale; you can tell it's exactly the same location, furnishings, Plasma TV etc. Apparently Chris was only living with her at HER apartment, and now Pacey has taken his place at the end. I guess this implies Pacey successfully started his own restaurant business in NYC as he had dreamed, to be with Joey.