I've got a copy of Raymond Unwin's "Town Planning in Practice", first published in 1909. These are pictures of town squares from that book.
The best squares convey a general sense of enclosure, resulting from a continuous ring of buildings. As you go into the square, you don't immediately see the way out. This gives a sense of restfulness to the town square, as a place to linger. This characteristic is shown in the old photos pf Stuttgard, Dresden, Piazza Erbe and Marienplatz above.
In Karolinen Platz, Cornhill and Max Joseph Platz, the roads dominate: the sense of enclosure and repose is lost.