A valuable question, with some pretty cool answers so far; but the question's got a lot of missing parts.
You haven't given us a whole lot of information about this. The answers so far make some pretty broad assumptions about your world; I'm guessing that those assumptions are probably reasonably good, but I want to call out some worldbuilding basics anyway.
Note that I am not going to address the aesthetic and purely creative aspects of your imagined world and realm and city. This is only an inquiry into the underlying mechanisms of reasoning.
This may be helpful. Considering the underlying realities can often ignite chains of thought that end up stimulating the creative imagination. Hopefully, this could do that.
However, I don't want to make you overthink the issue. Please ignore all of this if it doesn't help you.
OK. Here's a distillation of what you are telling us:
It's a fantasy world.
The city was planned as a political and religious center. Unpacking this, we can infer that
"Its geography is fairly simple - it's situated a little ways inland from a protected southern coast, with a river that flows through it to the sea. Two other towns flank it. The three were originally separate, but the capitol has grown outward and the edges have all merged. Most or all of the ports are located in the two adjoining towns, but most trading goes on in the capitol itself."
I'm not asking that you disclose any parts of your secondary world, but here are some very key questions. If you don't want to answer them for us - which perhaps you shouldn't - then at least perhaps you can ponder them yourself. Hopefully they can push you into thinking more deeply and precisely about the design of your city.
What impact would your fantasy elements have?
This is the big one, I think.
"Fantasy", as a genre, implies systems of magic and/or semi-transcendent nonhuman actors.
Sometimes these fantasy elements are not very consequential in terms of the shape and systems of the world: they are aesthetic elements, or plot drivers, but they don't really affect the generalities of ecology, politics, economics, and culture. They leave the worldbuilder free to proceed from close correspondences with historical precedent.
On the other hand, there are many kinds of circumstances and mechanisms of fantasy that will affect your world in a very significant way. If your concept of fantasy includes elements that will impact they way your world wags, then you will need to account for it.
Some purely invented examples (not, as far as I know, applicable to your world - just questions about how this can work) of how fantasy elements can modify your worldbuilding:
Are there populations (Elves, say; or Druids with the ability to make their curses bite; or dryads; or Ents; or whatever...) that make it difficult to clear forests for agriculture, or to build with timber?
Is there an age-old polytheistic clash between divinities of the Hunt and divinities of Agriculture? (e.g. Cernunnos vs. Ceres?) This is much more important than it sounds: Hunting-gathering and Agriculture are two very distinct, and mostly incompatible, modes of human ecology. Any fantasy element that sustains and supports the former is going to reduce the population of humans, because food surpluses per acre will be diminished.
Is there conflict between wizards and church? This is a staple theme in fantasy worlds, and it will create a fierce distortion in the politics of the arcane.
Are there formidable modes of mind-altering magic in your world? This can wreak havoc on the normal patterns of politics. (To take a trivial yet telling example: if you have practitioners of sexual magic, they could potentially exert enormous influence over the most powerful people. To say nothing of the ability to provide whatever sexual gratification an individual craves most, the blackmail possibilities would be absolutely splendid from an author's point of view.)
It can create a new kind, or class, of politically powerful individuals; you will need to work out who they are, and what their relations with other power centers will be.
Even if the end result is that the "Usual Suspects (the ordinarily wealthy and powerful in this sort of society) still come out on top, you have to deal with the change to their modes of exerting power.
Is your magic "technological"? Do you posit wind-mages who could improve the economics of sailing vessels? Is there magic that will purify sewage? That will lift heavy weights into place more cheaply than gangs of men and animals with cranes and derricks?
All of these things will change many aspects of your city, because they change building techniques, cultural predispositions, concentrations of economic power, etc.
And I'm not even going to discuss the possibilities of battle magic, since it's often considered here on Worldbuilding.SE - but you will certainly have to consider it.
Now, having briefly looked at merely the possible impacts of your notions of magic, let's look at some other fundamentals.
What's your climate?
Most older empires flourished in the warmer latitudes. In Medieval times, colder climates rose to parity, or even superseded the older warmlands as centers of cultural power. Answering this question will make a huge difference in your question of cities:
Do your city planners need to deal with ice and snow in winter?
Is it hot, so you need to build heavy masonry structures that stay cool in the daytime - and with flat roofs for summer nights? Or is it cold, so you need pitched roofs for shedding snow? These different kinds of building techniques will do a lot to drive the nature of the city.
Rainfall is very important. How much water flows through the city? How much of it is rain runoff, and how much is directed river flow? Are there canals for drinking water? Canals for sewage?
What kind of plants and animals are on hand? Draft animals tend to govern a lot of the expectations about street size and bridge construction.
Every civilization, great or small, pivots on one specific question:
Where does the food surplus come from?
What source of food provides a sufficient surplus? Presumably agriculture? How is it organized? Big slave-worked plantations? Smaller farms intermediated by a network of markets? Trade? (I know "trade" might seem ridiculously unstable, but it worked for Byzantium for centuries... and it works for us in the modern day as well. Ahem.)
Pastoralism - domesticating herd animals instead of plants - seldom seems to scale well to empire-level organizations. Yes, Gengis Khan's empire was the largest the world has ever seen: but it fell apart pretty quickly after he himself died.
You could, of course, make a case for a pastoral civilization without a lot of agriculture; but that would be a lot of heavy lifting, and you didn't hint at anything of the kind in the original question.
What level of technology does your world have?
Technologies of farm and building; technologies of weaponry and ships; do your metalsmiths work with poured bronze, a village blacksmith's forge. or blast furnaces? (Or tame/captive dragons?) Do you have the arch, or are your buildings post and lintel? Can you fire ceramics? Do you have the potter's wheel? What about weaving, spinning, knitting? The wool of which animals, or perhaps fibers from seeds or plants (flax, linen, hemp)?
What about brewing beer, viniculture, distillation of strong drink? Other mind-altering substances?
Leatherworking? Animal care? (Not just veterinary care, but things like farrier work, taking care of tack and harness, and merely handling the animals - I personally have 3 horses and it has taken me years to reach the point of being able to safely handle a 1000-pound animal who could easily kill me by accident.)
For that matter, you never characterized your world sufficiently to tell us that it's preindustrial! Again, it probably is; you would likely have mentioned it if you intended a steampunk or dieselpunk or postindustrial world. Still, that would add a whole new set of possibilities. :-)
And on and on and on...
What are your nation's politics?
Is this an empire (a political organization that obtains the wealth of subject peoples?)
Is it a kingdom?
Is it a city-state - a polis such as those of Classical Greece? Doesn't sound like it, but you never know. :-)
Is it a parliamentary democracy? A republic?
Is it a trading association (such as the Hanseatic League?)
Note that all of these forms of government tend to generate different kinds of civic layout and architecture. As a general rule, when thinking about what roads, bridges and canals get built; what buildings get located where; who inhabits the nice neighborhoods; and who lives in the slums, you will want to begin with the distribution of political power.
That this is a "planned" city does not change that basic calculus. The plans will be governed according to political influence.
What is your religion like?
Unless you plan on basically transplanting an historical model (medieval Islam, Zen/Shinto, 19th-centurey Victorian British Christianity, etc) with its assumptions, you need to think about the impacts of your religion.
Starting with its nature: Is this a polytheistic religion (like Egypt's, or early Rome's, or Shinto) or a monotheistic religion (like Medieval Christianity)? The answer to this has a lot to say about the internal distribution of power within the religious community, and presumably therefore the distribution of sacred architecture within the city.
Also, a monotheistic religion will be likelier to ignite crusades. Historically, "official" polytheism would sanction whatever the political leadership declared, but was not in general an activist tradition.
It was the monotheistic belief systems (which, oddly, all sort of got going circa 600 BCE in places as far apart as China, India, Asia Minor, and Judea) that turned out to be set up to stoke religious wars.
This is an aspect of belief systems that will have a lot of impact on your city and its enclosing civilization. The Church Militant (of any sufficiently chauvinistic belief system) is a much beloved worldbuilding device, presumably because the polytheists don't tend to provide the same grand sweep of historical activism.
There is one more question about your religion: Is it existential?
In other words, is this a system of belief that manifests itself as states of human consciousness, or do your god(s) actually exist within your secondary world?
This is an extremely important question.
How old is this city?
You said it was planned. How long ago? How long did the various parts of the plan take to complete? How many of the planned design elements were modified over time before completion? How much was abandoned?
Your city is a snapshot in time, after the original ideas and plans were made. It really matters whether it was initially built 100 years ago, or 500, or 800, or...
Well, that's probably way too long to be a helpful answer. But then again, perhaps it will add a little bit of illumination. :-)