Tell us a bit more about the world. What level of technology and society are we talking about?
Is there a god/goddess associated with justice/judgement? If so it could be the temple/palace of [god's name]
Not sure which bits would be of use (as I have a load of wordbuilding done), but..
There's no specific god of justice, as it's a monotheistic society. I suppose there might have been an older deity (the current religion has taken over the pagan cults that existed before, and so most of the older gods' names have been adopted as demons, characters from fairy stories etc).
Society-wise they are at a medieval level in technology, but more early-modern in terms of diplomacy and politics. This story is set on a group of islands, ruled by an hereditary monarchy, then a feudal system
(Nessam's post just got emailed to me whilst I was typing this so I'll answer here as well)
In terms of names, I'm avoiding making up exotic sounding titles or names for people as I don't like reading fantasies like that myself. I've used a lot of old terms, and where the legal system's concerned, mostly historical terms from the Scottish Legal System (for instance, my MC is the Procurator Fiscal and the chief judge in the country is the Lord Advocate.) The only really odd name I have is the one for the Parliament, which is referred to as the Sansiege. My feudal system is based on a hierarchy of castles built throughout the isles, referred to as the Great Sieges, so the Sansiege is considered a body within the feudal system even though it doesn't have its own castle. (before anyone worries about how dull this fantasy story will be, this is just background I made up for my own use, so I know how things work. Probably won't end up in the actual story).
I'm not sure what else people would need to know so sorry if I'm missing something obvious. Please just tell me and I'll try to explain better.
So what I was looking for was something other than 'Palace of Justice' that would sum up a building that's the hub of the legal system. My brain just isn't working to get it right now.