Rio is also a great place for architecture. The Petrobas building downtown looks like a Rubic cube and the adjacent Cathedral like a modern round pyramid.
My favorite place is a ferry and a short bus trip away from downtown Rio - the Museum of Contemporary Art at Niteroi. The space ship like building was constructed by Oscar Niemeyer who also designed the country's capital city Brasilia from scratch.
Take a look behind me: The wall of the building has the same inclination as the sugar loaf mountain on the other side of the bay.