Wilmersdorf was the center of Berlin, before the wall came down. Situated between Schöneberg and Charlottenburg, Wilmersdorf is still a very central district today. Though it is central, there is no hectic as in Kreuzberg or Neukölln. Still, you could get to those districts in about 20 min. taking the U-Bahn and Bus.
The apartment is very good located. There is a Bus stop in front of the house. U7-U9 Berliner Str. is in 5 minutes reach. All kinds of supermarkets are around.