I actually know something about this.
As others have said, it depends on a number of factors, including climate, whether the structures and surrounding terrain are eroding down or being buried by alluvial sedmenation or aeolian (wind) deposition, how dry or waterlogged the soil covering the ruins or structure are, temperature fluctuations, acidity in water or air, how aggressively vegetation can take over the ruins,what the buildings are made of, how tall they are, and scavenging or reuse of building materials by later peoples.
In a temperate, moist climate, environmental factors will start to wear away preindustrial buliding materials (stone, mortar) fairly quickly, but the worst damage is typically done by roots and human scavenging (the Forum looks as it does more from looting and scavenging than natural decay). Left on their own, stone or masonry buildings will eventually end up looking like mounds of rubble covered by trees and bushes in several hundred years. Roofs go fairly quickly and the upper courses of walls, lacking support, gradually collapse around the lower walls, effectively hiding them. It's important to know that most ruins visited by tourists have undergone significant excavation and clearing to expose the surviving masonry and often major reconstruction to make them look like buildings. Places like Mesoamerican cities generally just looked looked like featureless mounds of rock and earth covered with dense vegetation before excavation. Before aerial mapping and surveying, even trained archaeologists could walk over whole cities and miss major buildings.
We have no examples, but I'd suspect that a modern midwestern US city center with steel and glass skyscrapers like Chicago or Dallas would be recognizeable for millenia - probably at least as long as the Giza pyramids. A city like Las Vegas in a warm arid desert would last even longer. Not only would modern alloys and glass sheeting resist root damage, soil formation and freeze-thaw fragmentation, there are few natural process which could level or bury such a place. Of course, buildings and upper floors would gradually collapse creating a massive rubble mound with large sections of skeletal steel sticking out of the top and well preserved lower floors below. It would be cool to excavate. On the other hand, well-vegetated suburbs made of frame houses with brick/frame walls would turn to rotted rubble and vegetation thickets in only a few hundred years