Well, let’s take Henry II’s judicial reforms as a jumping-off point: he’s perhaps best known for the Assizes of Clarendon (which in addition to asserting exclusive royal jurisdiction over criminal cases and royal jurisdiction over land disputes, also created some of the first grand juries) where he established the justices in eyre – six judges from Westminster who divided England between them and would travel in a circuit from county to county, covering their entire circuit every two years. He also established permanent judiciaries in the capitol which would eventually be known as the Court of Common Pleas and the Court of King’s Bench.And this was pretty much how things went from about 1166 to 1285-1360, where the system of local justices of the peace began to replace the justices in eyre in terms of who does the majority of judicial work. 

So if we were talking about providing a judiciary for Westeros, I think you’d probably start with a system of itinerant justices who could cover a good deal of territory between them, and you’d probably stagger the numbers by the size of the territory involved: Iron Islands are pretty small geographically so you could get away with one, Stormlands and Crownlands could probably be covered by two justices each, Westerlands and Vale maybe three or four each given the difficulty of mountain travel, the North and Dorne would probably need 5-6 given the long distances but also the lower population density, and the Reach would probably need 10 or more given the size and high population.