To make the world feel complex, I would--always--start with the previous culture and people that the city sprang up around, though you don't need to go in any true depth. A rough outline should be enough. Even if the audience is never told a single thing about the lost culture, how they lived and what they did will vastly influence everything from architecture to room design.
For instance, a people with wings may not bother with ground floor doors, but concentrate on balconies to land on, or entrances on roofs. Depending on wingspan, rooms may be large and sparsely decorated. Then again, a race that climbs like a monkey may favor ladders, grabbing protrusions or walls built specifically to climb to another room instead of stairs. Dwarves, hobbits, and other smaller beings may favor spaces that feel spacious to them but cramped to humans.
Also, what and how they eat--think Skyrim and it's open fire pits without even a chimney versus a Victorian kitchen. If they focus on meat then more slicing tools may be left behind, but if they focus on corns or grains there would probably be tools that grind and crush. While the audience may never know the people who lived there favored pasta, old pasta making tools scattered about (especially in a visual medium like comics or games) would be an interesting touch. Since all these things could easily be used by your characters as they roam the ruins, knowing what might be still hanging around would be important.
Decoration, too, is unique. The difference between Egyptian and Aztec hieroglyphics and chosen patterns and colors, for example. What deity is worshiped may also have a lot to do with decoration, and, of course, there are those all important worship spaces like the Japanese altar or the chapel found in castles and fortresses. Temples alone may not house religion, and religion often influences design schemes of both architecture and decoration.
I assume you already thought about class--the rich and poor having different design schemes--but families and clans may have them too. If your lost people would have had insignias, banners, or other markings of their importance, it might still be around in rotting tapestries or carved into stone. It might even be found in strange places, like wrought in metal over an inn door that they owned but employed others to run. Families and clans can consist of the poor as well as the rich, so different insignias might be found in surprising places.
Then there's just the architecture itself, which will be based on the people and their culture as much as the environment itself. For instance, do the keep grandma in the attic or in a wing or room of her own, or is the whole family liable to sleep in one room? Do parents and children share a bed?
Do they marry multiple spouses and all the spouses bundle up in one huge bed? Do spouses sleep rigidly separate, with a special bed or altar for conjugal visits? Do they live completely separately, only meeting in a special garden? Are children banished to one part of the house or given free reign? Are they put to work as soon as they're old enough to perform simple tasks or schooled, or is the answer to that class-based? Do they bury their dead in graveyards or beneath the floorboards, or do they just burn them or give them to a river? Do they have statues everywhere, or do they have no realistic images because they're superstitious about evil spirits taking them over?
Environment is also key to design--think stilted houses in flood planes, rounded huts or buildings in areas of high winds, sloped roofs in places of heavy snow, and so on. You can also add interest by showing local elements in design--a certain type of black stone, or perhaps a lot of hard-fired red clay, etc. A sun worshiping race may have a city that radiates out in spokes from the center like rays of the sun, while one that grew bigger than the space it's crammed into (think Sedona or San Francisco for cities with space issues due to environment) may be cramped with narrow streets and buildings that go several stories tall.
The nifty thing about humans is we have some serious pattern recognition abilities. When you have consistency in your design of the city because you know what and how things were used in the past, it doesn't matter if whoever you are maneuvering through the ruins knows anything about them, if the walls have fallen down, or if only parts of structures and scattered items are left. They're going to recognize the same wrought iron wolf's head and wonder what it once meant, or the constant use of blues and greens in tapestries, or come to expect to find holes for storage in the kitchen of every poor man's house.
And because they can pick out those patterns, it'll feel so much more real and alive to them, and they'll be as curious and intrigued as your characters.
We don't need to know gross national profit or marriage customs or biggest exports or even the system of government (beyond really obvious leftovers like execution areas or jails). But a sketch of the culture-that-once-was will really enliven and add realism to your creation.
