This area stands out for museums, the park of El Retiro and its Lucifer’s statue; among other things. I don’t usually hang out around this part of the city. Although, I’ve found some nice places on internet.
Bar on Rock. Opened all days except tuesdays till 2:00 am. Looks pretty nice and clean Check their FB page and website (Atocha Renfe train station or Menendez Pelayo metro statio, line 1, light blue).