This area worked very well for us. The apartment itself was great, there are many shops and markets close by, the metro is right there, and Gran Via is just a couple of minutes walk. So no problems at all. The immediate area isn't particularly pretty (especially compared to other parts of Madrid) but we always felt safe. And I have to say that we found people in Madrid to be very friendly!
Madrid is incredibly beautiful, and we felt like we needed a lot more time to get to know it better. I guess we'll just have to come back!
Ten Weeks in Spain: Adventures in Spain with our three year old.