It's up to you.
One of the joys of roleplaying games is that as the GM you have a large degree of flexibility in what you do.
Flexibility versus Preparation
If you prepare a city with a lot of diagrams and an actual map, that's great. You'll be able to come up with stuff without even having to stop and think about it because you've already charted it out and written it down. However, it also strips away some of the narrative flexibility unless you're willing to go back and ignore previously written stuff.
Take, for instance, a chase. On one hand, you could design it to go from Point A to Point B on the map, which is great, but that takes away some of the decision making. If the players get beat up along the way, you have to decide whether or not they even make it to Point B, or fudge. If you're working in a narrative format, you could decide that the players make it to their destination after taking a little beating.
Of course, you've also got more preparation if you have a mapped out city, which means that you can plug stuff in as needed. Just be sure to leave some white space to fill in the gaps; there will be some buildings of no interest to adventurers in every city, and having a few nondescript areas allows you to then later label them appropriately on map and incorporate them into your adventures.
Of course, you don't have to show your players the map, and it can be strictly for your purposes. In one of my Shadowrun games I kept a map of Seattle with a list of places they'd done runs/met Johnsons/etc., and it worked well to keep my mind fresh and allow me to come up with inspiration.
Narrative versus Setting
Another thing to consider is that designing a city may not actually help your campaign along. If you're doing an urban exploration campaign, like in the plot of the first bit of the original Neverwinter Nights, then having a really detailed city can help the plot because players will have the ability to explore and adventure.
On the other hand, if you're playing a standard Swords and Sorcery dungeon crawl, I wouldn't worry about having cities with details; if it's not the point of your game you shouldn't waste time on it. Not only does it tempt you to bog down the adventure with details that players don't care about, but it's a waste of prep time that could go toward making the core focus of your game better.
Remember, focus on what your game wants to do, and don't worry about going into specific detail on everything just because the setting lends itself to it. Similarly, remember that planning often goes unused, and don't be afraid to add something on the fly just because you haven't fully planned it out.