Though only tangentially related to the actual question posed, I do not think that an advisory council should be distributed between the cities. Firstly the government of any great city requires more or less all the expertises listed, and secondly, the point of advisors is to be accessible when the Emperor needs them. So unless magical videoconferences are widespread, the Council should sit in the capital, and the other cities should have lesser councils of similar composition.
The actual composition of the council is mainly subjective. It depends on the setting details: What are the main economic activities in the realm? How magic works? (that would for example decide if there need to be separate Councilmen for Magic, Planar Protection and Religion)
You should also think about the powers the council has:
1) Is it a purely advisory body, providing information and advice, but always leaving the decisions (and their execution) to the Emperor?
2) Or are the members more like ministers of a modern government, wielding authority given to them by the Emperor, and directing bureaucracies?
3) Or can they vote about things?
(So if the Emperor wants to levy a new tax, in case 1. He asks the Councilman of Finance and the Councilman of Trade, deliberates on what he hears, and then commands other subjects (provincial governors, imperial freedmen or whoever) to execute what he decided. Whereas in case 2. He only commands the Councilman of Finance to levy the tax, who himself fleshes out the details (what cities should pay and to what deadline, census, etc...), and directs his underlings (tax collectors and accountants), and then reports back to the Emperor.)
There is no one side-fits-all formula, so I will present some examples I made up hastily:
Empire with irrigation around a river (think ancient Mesopotamia):
This empire has an agricultural heartland of ancient cities, centered on a fertile riverbed. Around it live subdued Hill Cities and Pastoral Tribes. The Emperor is also a High Priest and is held a Descendant of Gods. He rarely leaves the capital, leaving conquest to his battlefield commanders.
The High Council is composed of Men from different statuses:
- Three Marshalls: These are field military commanders, commanding one army each by geographical subdivision.
The Overseer of Channels: A great minister, responsible for a large staff of civil engineers, directs operations to keep the lands irrigated but not overflooded. He has special judicial authority in all water-related disputes (eg. when the people of a village divert water from the canals of another), and direct public labor to constructions.
The Overseer of Levies: A great minister, he ensures that the Hill Cities and the Pastoralits contribute the required number of soldiers to the Imperial Army, and that the army is well equiped, He balances the Marshalls, who are heroes and tactical masterminds, but can not feed their armies alone.
The Overseer of Magicians: A quite great minister, overseeing the guilds and associations of magic users. Special judicial authority in charges of dark magic usage (necromancy, etc...)
Overseer of Geometers: An important minister, deals in land ownership and boundaries.
The Overseer of the Court: An important minister, runs the Imperial court itself, its ceremonies and the goods needed to maintain its splendour.
The Overseer of Envoys: An important minister, he manages foreign relations and emissaries.
The Twelve Delegates: They are the representatives of the core cities. They are not specialists, rather local politicians and lobbyists.
The Master Diviner: He is not a minister (does not have a ministry under him, only a few acolytes), merely a advisory specialist for predicting the future and expiating prodigies.
The Master Physician: Attends to the personal health to the Emperor, and gives advice the Delegates and Marshalls to prevent epidemics.
The Examiner of Pleas: An advisory legal professional. He is not a judge, only checks supplications whether they are worthy to the attention of the Emperor, and gives advice.
Note that there is no minister of finance: This is a society before money was invented, and the needs of the administration are collected for the court in kind under the Overseer of the Court and the Levies. There is also no supreme spiritual and judicial authority in the council, as these are the Emperors special prerogatives.
So you could think about how the system in your country came to be and evolved: In my case it looks like this: There were city-states in the heartland. One conquered the others, and its King became Emperor, and its patron supreme god. The Master Diviner and the Master Physician were in the entourage of the King before the conquest, just as the Overseer of Court and of Envoys were previously royal officials. The next emperor invited the Delegates into the council to help rule the cities peaceably (wars were frequent previously), and created the Overseer of Channels and of Geometers to delineate the territories and irrigation water claims of them. The next emperor conquered the Hill Cities, and created the Overseer of Levies to help control them. The next emperor left the system alone. The next was slothful, and created Marshalls to command the army in his stead, and the Examiner of Pleas to spare him the nuisance of dealing with appeals in petty cases. After a dangerous demonic outbreak the Overseer of Magicians was added, and the system was mature.