In many parts of the world the "modern" cities were built upon the old cities meaning that some of the richest areas for excavation and research were within reasonable distance from "modern" cities. Hundreds and thousands of years of cities built on top of or expanding and retreating over the same area. In fact it seems like every year you read about some construction company hitting an old aqueduct or a graveyard or something else.
It seems the same from Europe to the Middle East to China. Then I look at major sites in South America and it seems that they're nowhere near any modern cities. These were big, thriving cities and apart from a couple that may have been abandoned for various reasons there should be some amount of them that were continuously occupied and built over. Is that just my perception or is there something I'm missing?
A few notes on the Andes region:
As has been mentioned, Cuzco is a great example of a city with a consistent existence across time periods. It has been one of most significant cities in the region since at least the 1300s.
During the Spanish invasion, locals were frequently relocated into consolidated, organized settlements (reducciónes) to make them easier to manage. This moved millions people away from the towns they and their families had lived in for centuries.
This was not the first time this "artificial settlement" occurred. The Inca, Wari, and, to a lesser extent, the Tiwanaku empires all had their own conception of an ideal city and likewise relocated folks to suit their political needs.
The harsh nature of the Andean environment means that the same sites will remain inhabited but not necessarily with any continuity. Take the city of Tiwanaku. People have been living in the exact same place for 3,000 years, and for a few hundred years it was one of the planet's most important cities, a cultural and economic capital. Time went by, the plain got drier and harder to farm, and, the Inca built ugly bureaucratic buildings on the old temples, but folks still live there. It's a tourist town, but a town nonetheless. Lima, on the other hand, is dotted with archaeological sites, some rather imposing, but is bigger now than it's ever been. Yet the connection between these settlements is purely spatial.