A city starts as one thing. In a fantasy setting it's usually a tent on a hill. It is usually out in the open and not clustered away in the trees. Between this place of central government a foot-beaten path forms to the common areas where peasants live and work. Water must be available for them nearby.
In the next stage one of several things can happen. The civic town structure can remain and be expanded upon, or a manor house appears. The manor ( the estate, not just the house ) would average ten families. Nine would work the land to provide for the needs of the tenth family ( the nobles ). This tenth family would do some-thing other than work the land. In most cases their duty would be to protect the people, but every manor has its own unique history.
At any rate, Main Street would form. This might not be the central street once the population starts rising and more land is required, but at the start Main Street is the place of labor and shops. The smithy, the saw mill, and the fishery are usually not part of Main Street as they can annoy citizens with noise or smells. Main Street is quite normally on the water source directly, if it is a well, or said water source is built into it in some way. Remember, Main Street has to be the cleanest and most sparkliest street in town. It tends also to be the straightest, though that isn't an absolute rule.
Other housing exists either on, or near, the shops of Main Street for residents. Eventually, these tend to integrate as the population of the area grows, forcing the buildings to become multiple stories in height.
Defenses tend to grow with the city. At first, a cow fence. Then, palisade. Then, wall. Behind each one of these is either pasture or a path where militia or other soldiers can assemble. As the walls grow out these circle / eclipse paths become established roads which other houses are built around. They almost always connect in some way to Main Street which grows its own Town Square because of this. Even more than Main Street, the Town Square becomes the prettiest place in the city. Trees; statues; fountains; shrines right next to the square. I'm sure there's no lack of imagination here.
Keep in mind, though, "Water is Life." Citizens won't want to move to a place that doesn't have access to fresh water. Paved roads with the ability to channel waste water become important at this stage regardless of manors, halls, keeps, or castle walls. If the people are drawing water from the river, rather than a well, then the waste water will have to dump down-stream, if at all. Cess pits and cess pools are common in the early stages and located quite far from the town proper. They are also, generally, at the lowest elevation possible if flooding is a danger, if not an elevation lower than say, "Where the wealthy citizens live."
Cities...primarily grow in circular shapes from these centers: Water Source, Manor, Square, Main Street, Primary Work House, and the highest topographical elevation. I need to be careful about saying that because land formations such as boulders, sacred groves, or the local cemetery could change things.
...and just to make things even more complicated(!)...there are the special building projects.
Civil services such as parks, fire-fighters, law enforcement, temples, and watch towers don't cluster in one place. The citizens have to be able to access these places on foot so the 'spaces between the streets,' which become blocks, will have buildings torn down or re-purposed to provide for the needs of the gentry.
"Roads are not for cars. They're for the military." Main Street is usually the nicest path, but once it's stoned it also has to be broad. Guards and soldiers have to be able to move quickly to what-ever wall section or area that they're defending so Main Street should be able to connect well, if not perfectly, to two opposite sides of the town. Castles, of course, are usually designed to have only one entrance.
Farms are located out-side of town. The end. Fields require space and nobles consider any-one with horses as able to ride into the protection of the walls quickly.
Let's talk about harbors. Harbors are one of those tricky-city things. Obviously, there are docks. In the early days of the settlement fisher-men bring in their catch. Right next to the dock is the fishery for cleaning the catch. The catch moves immediately to the market for sale. As the population size of the city increases, how-ever, storage will be required so store houses are built.
Docks bring ships and trade. Slowly the storage areas begin to squeeze out the fishery shops. The reason that all of this is important is because the citizens have to be able to live near the docks / harbor in order to work there. So there is almost always a road behind the docks ( and the ware-houses once they arrive ) that takes the shape of the river where the piers enter the water. This road is almost always for lower class working citizens. It may, there-fore, connect to Main Street by other roads, but not directly and almost never to the town square.
But, it's not my city. It's Kazou's. These are just some thoughts. I suppose what I should really say is, "Do what you want and have fun." ...and don't forget to share your results. I'm kind of interested too.