In Pokémon Black, White Forest is replaced with Black City. The difference between the two, to quote Serebii.net: "Black City is a city that is completely exclusive to Pokémon Black. This city will feature many characters and tasks that will not occur in Pokémon White. In it, you'll find numerous trainers to battle and numerous shops selling items." as opposed to the new wild Pokémon encounters found in White Forest.
Source: Serebii - Black City/White Forest
Hope this helps!