It will take you around an hour, like it did to me, to visit all of Mayo Square.
Of course I just entered to the great Cathedral, but if I were you, I would go on the guided visit, which lasts three hours and it can be done on any week day.
Near Mayo Square, taking the so called “South Diagonal”, we step into the Quarter of the Lights, on Peru Street.
There, we can find the very interesting tunnels where the Public Buildings were. To get in there, you have to pay approximately one dollar.
Continuing at Defense Street, we can find the National Historic Museum. It has a viewpoint at its tower and a gallery with objects from the Virreinato period, and from the time when Argentina got its independence.
Continuing on the same street, we get to Lezama Park, a beautiful place that reminds people from Buenos Aires to the writer Ernesto Sábato and many of his books, which frame the city in a very special way.
Down on Brazil street, between the others two I have named before, we find one of the most interesting churches of the city, the Orthodox Russian Church. This place has five domes with the form of an onion, and its cross looks to the East side of the great Buenos Aires.