Here is a map of Moria:
On this map you can see the different regions of Moria. In my oppinion a division into five parts and therefore five cities would be usefull.
-Dimrill gate
-Halls of Moria
-Old Moria
-Mines of Moria
-Hollin Gate
Therefore the map should look like this:
The only access to Moria from west would be the the Hollin gate. From east it would be possible to enter as it is possible to enter Mordor near Minas Morgul.
There would be in the middle of Moria some rivers which would depicture the underground rivers and lakes. (You maby remember the lake in which Gandalf and the Balrog fell.)
The only access to Old Moria would be through the Dimrill Gate. This would also suit to the lore, because in the second hall, which would belong to the region of Dimrill Gate, you have to decide whether you go to the great halls of Moria (in the north) or to the Old city of Moria (in the west). You can see this on the map

.
It would also been shown, that the fastest way through Moria don't go through the Old city but through the halls of Moria (The way the fellowship goes)
Therefore such a division and placement would show Moria as it is in the lore.
Edit: The owner of the different cities:
The orcs were not united in Moria.
Hollin Gate:
There were the Orcs in the west, who had nothing do do with the ootmm. They only tried to kill and maraud in Dunland and Eregion. They mosttimes uses Wargs and were under the command of a local war lord.
Mines of Moria:
There were the dark creatures who lived in the deep mines. The Balrog was the most famous of these, but there were also other not so strong but even older creatures digging there in the earth. Gandalf speak of them when the fellowship is in Moria.
Old Moria:
Old Moria was inhabite by Orcs which were also under the rule of a local general. They fight against the ootmm.
So this three cities should be rebel cities.
Halls of Moria and Dimrill Gate:
This hall were under the controll of the ootmm. But they feared to invade whole Moria because they feared the Balrog.
Edit: Balance conciderations:
There could be other building possibilities for the different races:
1. Dwarves can build all buildings they have in Moria
2. Orcs can build only some very basic buildings in Moria
3. Elves and Humans can build no buildings in Moria
Come on, it is totally not suiting to the lore that the elves of lothlorien can make a copse out of the halls of Moria.
Orcs also don't really build "cities" in Moria. They used the space to live there and tried to find Mithril but they don't carry wood in the mines to build up barracs or houses.
There could be one unique building:
Balrog of Khazad-Dum:
Effect:
-40% income
-50% growth
This building could be destroyed after an historical event.
Therefore it would be possible to restaurate the Realm of Khazad-Dum.