The "squares" mentioned are not official Squares as such. They're more a pet name used to describe the areas.
There's Centro Commercial (CC) La Hoya, at the cross-roads in the Old Town in PDC. And in the middle of the La Hoya is an open, square area.
Dito for CC Montana Tropical: there's a square area in the middle of a few pubs/businesses.
CC Olivin also has a square, but I've only ever heard it called 'Freddies Square'

Can't recall off the top of my head what the area is called where Arthur's and the Whale and Ale are, but it'll be CC something or other I imagine.