Smart, resourceful, and more than willing to hear counsel from others, Tyrion truly is the ruler Westeros needs.
He might need a surname change, as the Lannister name is surely a bit tarnished by this point.
Tyrion Lannister (who has the most screen time in GOT) essentially ran the realm once before, as he put out numerous fires set by sister Cersei and nephew Joffrey.
No doubt, he would make another great Hand of the Queen if Dany takes the kingdom, but if things went south there, Tyrion could definitely rule the realm with little more than Varys at his side.