Who do you consider the greatest known ruler of each of the Seven Kingdoms? Someone we might add the appellation ‘the Great’ to.

Good question! Well, I haven’t finished my series on the Seven Kingdoms, but I’ll give it a go from what I’ve done:

• the North: in terms of the magical-meta plot, you’d probably have to give it to Brandon the Builder, who won the Battle for the Dawn, built the Wall and the Night’s Watch, and then founded House Stark. But if we’re talking purely politics, it’s probably Theon the Hungry Wolf for completing the unification of the North, throwing back the Andal invasion, and successfully pushing the Ironborn out of the west. 
• the Vale: well, the Valemen would probably say Roland I, who ordered the Eyrie be built or maybe one of the warriors like the Old Falcon or the Talon, but I’m going to go with Osric V, whose more practical reconstruction of the Bloody Gates kept the Vale safe for thousands of years.  
• the Riverlands: Benedict I Justman hands-down. Brought the Riverlands out of the chaos of civil war, unified the Brackens and the Blackwoods, provided equal justice to all, and founded a long-lasting dynasty that brought the Riverlands to its historical apex. If Bernarr II had been more like Benedict the Just, the Riverlands might never have lost its independence. 
• the Iron Islands: well, the followers of the Old Way would probably say Qhored the Cruel, but I’d go with the three Harmunds, who somehow managed to incorporate the Iron Islands into a continental political system that had previously viewed them hostis humanis generis, or maybe Qhorwyn the Cunning, who best exemplified the New Way. 
• the Westerlands: probably Tyrion III and Gerold II, who brought the Andals into the fold and used them to reinvigorate the Westerlands and provide the raw fuel for the unification of the Kingdom of the Rock. Without them, the glories of Cerion or Tommen I or Gerold the Great would not have been possible. 
• the Reach: not even a contest. Garth VII the Goldenhand, a “giant both in war and peace,” who defeated every single one of the Reach’s enemies in detail, turned them into his allies and kinsmen, and left the Reach with seventy-five years of peace. Possible contender for Greatest Westerosi King Ever, given that he did all of this without any dragons. 
• the Stormlands: haven’t gotten to this one yet, but probably Arlan III, who built one of the largest empires in Westerosi history and came closest to actually winning the Great Game. 
• Dorne: Nymeria. Led her people across an impossible trek, founded not merely a kingdom but a nation, unified that kingdom through war and peace, held it against invasion and civil war.