An intricately detailed, 19th century building spanning the width and length of a block in Balvanera, the Palace of Running Water must be the world's most impressive clean water pumping facility. I can't imagine it even has a competitor.
Around the corner from the ostentatious Palacio Paz is the much more refined Palacio Noël, home to the Museo de Arte Hispanoamericano Isaac Fernández Blanco. The palace would be worth seeing in its own right, but together with the museum, it's one of Buenos Aires' cultural highlights.
Near the Plaza de San Martín in Retiro, the skinny Iglesia del Santísimo Sacremento is not as famous or conspicuous as so many other landmarks close nearby. But as long as you're in the area, it's worth taking a quick walk through one of Buenos Aires' prettiest places of worship.
In the 19th century, the wealthiest corner of Buenos Aires wasn't Retiro or Recoleta, but Barracas. Over the decades, this southern neighborhood lost its former glamor but recently has been showing signs of a resurgence in popularity.