First Encounters of the Close Kind - S3-E10
Plot hole: Joey tells AJ that her Mother used to read "Little Women" to her, and in fact named her 'Josephine' because "Little Women" was her favorite book. But in a previous episode when Joey and Dawson visit her Mother's grave, the gravestone has printed 'Lillian Josephine Potter', meaning her Mother already had Josephine as her middle name. So naming Joey 'Josephine' wasn't only because of the book "Little Women"; her Mother more likely named her that because it was her middle name.
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.