Florence, Milan, Venice, and Genoa were the most important city-states of Renaissance Italy. This distinction is the chief attribute shared by these four cities.
Of course, that's a bit of an intrinsically subjective statement. There were several major players, and it is difficult to quantify something as nebulous as "importance". Nontheless this particular grouping is quite common. These four cities are pretty much universally regarded as occupying the heart of the north Italic city-state system.
As emphasised in different but complementary ways by such authorities as Braudel, Lane, and McNeill, this subsystem of city-states - centred on Venice, Florence, Genoa, and Milan - anticipated by two centuries or more many of the key features of the modern interstate system.
- Gill, Stephen, ed. Gramsci, Historical Materialism and International Relations. Vol. 26. Cambridge University Press, 1993.
The British urban historian Peter Clark:
By the close of the Middle Ages, the urban network of northern Italy was dominated by four city-states: Florence, Venice, Milan, and Genoa - often in fierce competition with one another.
- Clark, Peter. European Cities and Towns: 400-2000. Oxford University Press, 2009..
The Dutch professor Luchien Karsten:
The new system of city-states was mainly established in places such as Venice, Genoa, Florence, and Milan.
- Karsten, Luchien. Globalization and Time. Routledge, 2013.
The late French historian Fernand Braudel:
Quite clearly in the Mediterranean in the fifteenth and sixteenth centuries that centre was a narrow urban quadrilateral: Venice, Milan, Genoa, Florence, with conflicts and intertown rivalries as the relative weight of each city changed.
- Braudel, Fernand. The Mediterranean and the Mediterranean World in the Age of Philip II. Vol. 2. Univ of California Press, 1995.
As well as popular history writers:
Chief among the Italian city-states were Florence, Genoa, Venice, and Milan.
- Hazen, Walter. Renaissance. Good Year Books, 2004.
Such statements reflect the historic weight of these four cities, as the centre of their respective city states.
The building in question is the Palazzo Eridania, built in 1908 by the architect Richard Haupt. It is situated on Corso Andrea Podestà, 2. As far as I can tell there is no deeper significance in the choice of decorations.