In short, I want to figure out some sort of realistic relationship between the Embassadors, the traders, and races. What sort of connections would make sense for a Gnomish rug merchant? (or whatever) Or, even better, how would I approach such a problem?

Any suggestions would be appreciated.

Also, as you get further away from the center of the city (where I presume the main roads all meet somehow) you get further away from contact with other races, so that the city is shaped a bit like a star, with racially distinct rays heading out along the roads. Nearer the center, there is a more formal border between the various sectors but you're closer to that border and it's easier to cross it without getting mugged or arrested.

You also need to add another layer of government, since each of the sectors would want (probably need) individual and semi-independent government and police forces. These sector governorships would be subordinate to the Embassies, which would represent policy at the national level, but also have a fair amount of independence. In other words, the ambassadors wouldn't typically have any more power over the local government than they would over any other local officials elsewhere in their respective nations. Your Governor would correspond more to the president of a international council, and would have no binding authority outside of the Governor's House (here assumed to be a centermost precinct of the city).

The Governor would have no (official) dealings whatsoever with merchants and such outside of the Governor's House. The main fuction would be to preside over and enforce the house rules of international diplomacy carried out within the central precinct itself. The Embassies, on the other hand, would probably have a good bit of influence over their local governments and thus over the merchants, and it would make sense that powerful merchants would have bribed some of the ambassadors (above board) and a few might even have subverted persons with influence/authority inside the Governor's House. But that game would be dominated by agents of the various national governments, either in cooperation with the Embassies or working without official cover (no diplomatic immunity, in other words).

To wit:
-Are the "boundaries" formalized or just the result of custom? How free are beings from various races to move from sector to sector? Even if they can move freely, does say, a Gnome meandering through the Elf sector raise suspicions? Would he be met with disdain or outright prejudice? Would no one give it a second thought?

-What are the overall relationships between races like? Are they prejudiced? Amicable? Peaceful but suspicious? Hostile?

-Does the political power of any given race relate to the size of their "slice" of the pie?

-Do Ambassadors meet as a body (like the UN)? How much power do they have? Are they mere mouthpieces for their races or do they wield genuine political leverage?

-Are there Trade organizations? Are they open to all races or are there separate one s by race? How much political power and influence do they have? How does one become part of a Trade organization? WHo runs them? What is their relationship to the Ambassadors? How much influence do they have on the selection process?

-Is each race allowed its own military forces for defense of their area? Do the Ambassadors get personal guards? Who makes up the military forces controlled by the Governor? Are they from his own race or a mix of others sworn to be independent of all races?

You have the central governor, I assume, is the head to the city, period. Then you have the representatives of those races under that. But perhaps, you might elect one head governor and then have sub-governors (for lack of a better term) which deal directly with their own districts. To seperate them wholly by race alone seems to be the start of the trouble right there, you get into inequality disputes, inter-marriage problems, etc.
To have one race hold the highest position is just asking for trouble with the others, especially if his policies infringe upon the other races' liberty, goals, etc.

Maybe you could have a unique governorship where it's divided between representatives of those races: one for the humans, one for the elves, one for the dwarves, etc. What if the all suddenly disappeared or whatever. Where would that leave the city? What would the citizens do? What would rival city-states do when they learned about the turmoil?

It is even designed in concentric circles.

It is populated almost entirely by public servants. It is a city with no good reason to exist.

How did your city start? What was the natural resource that caused people to settle there? I would find it more plausible if there was some sort of 'parley centre' -- like Thingvellir, the valley in Iceland where the first parliament was formed -- surrounded by satellite communities. One of the problems would be the administration of law. Where there would be different punishments ascribed for different crimes in the differing cultures, these would be worked out within their own communities if the offense was internal. However if the offence crossed-over the cultural boundaries, it is sensible to have a mediator able to make a ruling that satisifies all the parties invoved.

This position of 'governor' would have to be impartial. If not, then it would not be used or worse held in contempt considered illegitimate. If every faction is vying for the job, there must bring some perceived benefit. You must ask; what is to be gained form having your own people in the position? It may bring into question the impartiality of the position. Is it corrupt?

PS: Read about that valley here.

I think what you are leaving out is history. The city firstly needs something to ground it. Like hoptoad mentioned, tell us why these races settled there in the first place. Think of reasons why people move to another state or continent; religious freedom, exploration, banishment, or just general freedom. Your city will be much more believable with some historic groundwork.

I would also think that the city was probably turned multi-cultural over a period of time, which would lead to the various sections of the town being added upon and segregated (for lack of a better term). If you look at large cities, take New York, San Fransisco, L.A. Chicago etc... they all have different sections that are mostly populated by one nationality or another.