On Monday the trio took to the cobbled streets of the city's San Telmo district to browse antique stalls surrounding its main square, the Plaza Dorrengo. The famous 'barrio', known for its colonial-style buildings and old churches, is one of the oldest in the Argentine capital.
The You Wear It Well singer had covered up against the early autumn southern hemisphere sun in a panama-style hat and all-white ensemble, while his former model wife was cool in outsized shades and a sun dress. Later, the pair relaxed over a romantic lunch in the garden of their hotel.
Ahead of Rod's gigs later this week the family will no doubt be keen to explore other parts of the fascinating city. And Penny's stint on Strictly Come Dancing could serve her well if they head for the famous tango district of La Boca, where the dance form was born at the end of the 19th century. There, against a backdrop of houses made of metal sheets painted in different colours, street performers
demonstrate the dance and often encourage visitors to take part in the action.
The Nueve de Julio Avenue - the widest road in the world at 120 metres - may also be on the couple's agenda, along with the Casa Rosada, Argentina's pink presidential palace.