I'd advise you against doing more work than you have to, but that's what DMing is all about.

One trap I'd suggest you NOT fall into is giving every function of the city its own district. For example, don't have a Tavern District or a Shops District. Walking 30 minutes to get TO a tavern is irritating to every last commoner living in the city; if some foolish government passed a law like this, expect unauthorized speakeasies to be popping up in homes and after-hours shops inside of a week. Similarly, you might put all the major churches together, but in a truly big city expect there to be a few shrines outside the Holy District.

Instead, ask what makes SENSE to be defining a district. A major bazaar by one of the gates? The palace? Other centers of power? A magician's academy? A warrior's academy? Certain industries, like tanning or brewing? Where is there a benefit to congregating that outweighs being evenly distributed throughout the city?

Once you've got whatever defines the district, populate it with the appropriate support buildings and personnel. A palace district, for example, will likely be surrounded by embassies, homes for palace servants and barracks for palace guards, high-end inns and restaurants catering to the well-to-do, upscale gambling clubs, lawyers, heraldry designers, jewelers, perfumers, etc. A magician's academy might be surrounded by more than its fair share of coffee shops, brothels, curio shops, bookstores, bookbinders, ink-makers, arcane-component vendors, and firefighters. The brewing district will have lots and LOTS of public houses all with signature labels, but also housing, good wells, bottlers and barrelwrights, warehouses overflowing with hops and barley, and so on. A single large cathedral to the city's patron deity might be surrounded by housing for staff and religious students, libraries for scholarship, the most faithful commoners in the population... and probably quite a few things representing the foibles of the religion.

Divisions can also suggest or be highlighted by separate districts. If the local government shows a lot of tug-of-war between Crown, a House of Lords, the Church, and the Army, put the headquarters for these factions at different districts -- ideally on opposite sides of the city, or on hills where they can glower at each other across the gaps.

Note that not every industry need define a district, or vice-versa! For example, carpenters probably don't need their own district. They're needed everywhere, and don't much benefit from concentrated factories. Similarly for police and firefighters, midwifes and doctors (though one big hospital might be called for), et cetera. Furthermore, not every district needs a defining element! Make many of these districts overflow (suburbs). Because they're a long walk from anywhere important and don't have industry of their own, these will be the slums, with substandard tenet housing, a poor and disgruntled population, high crime rates and low hopes. Some of these districts will just have grown up that way, but others may have a forgotten or obsolete purpose -- say, a former market that used to be around the Old Wall before the New Wall was built further out, or a church that has since been banned.

By the way, while all of these districts have some form of tavern, the character of the taverns will vary from district to district. Expect something appropriate for traveling merchants by the gates, with emphasis on lodgings and hot food for travelers who've been too long without. The palace, as mentioned, will have the upscale restaurants and gambling halls. The academies' taverns will be more like coffee shops, and a tavern near the headquarters of the City Watch will be a cop's bar. Decorate and populate each accordingly.