Continuity mistake: When Pacey is driving Joey back from Boston in the morning, they start talking about what happened. Every shot of Pacey or Joey from either side shows a heavily wooded forest (mostly pine trees it looks like) in the background. But when Pacey abruptly veers off the road to the right and parks; suddenly the landscape on Joey's side is barren with a huge lake, and no forest or trees except a few they just passed on the curve. The pine tree footage was probably added in to make Wilmington, NC look more like Capeside, Mass.
Revealing mistake: When Joey and Pacey are talking in the car as Pacey drives them to the Train Station, you can see at least 3 lanes full of cars and a great deal of traffic behind them. But when Pacey suddenly turns right, off the main road and into the entrance to the Train Station; you can see that suddenly the main road he has just turned off of is almost completely empty of any traffic in either direction, except a truck that drives by at the last minute. It also appears to be a smaller road. Apparently the scenes with their dialogue in the car were shot with background video that wasn't the actual location.
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.