To some extent, the answer depends on your definitions of "abundant" and "major city." Generally, the supply of water needs merely be adequate to support a population, not "abundant," so I would argue that the situation you describe is rather common, with perhaps hundreds of important cities present and past thriving despite their distance from a major river or freshwater lake. The presence of "abundant" water does contribute to a city's growth, however, because historically, water enables trade, and trade in aggregate brings prosperity, and prosperous cities will grow.
Human settlements number perhaps in the millions, but not every camp becomes a village, not every village a town, and not every town a great metropolis. Cities grow because cities prosper, and while access to water was historically important, it was not for the reasons you propose.
Do not conflate cities and their civilizations. Civilizations depend on agriculture, and agriculture depends on water, but almost by definition little agriculture takes place in cities. But even in the case of agriculture, many pre-industrial civilizations were able to divert springs, store floodwaters and runoff in reservoirs, and supply agriculture through canals.
To be sure, water is necessary. Mesopotamian civilizations shriveled when the Tigris or Euphrates shifted course, and parched Dodoma is Tanzania's capital largely on paper partly for its unstable water supply. But "abundant" water is not sufficient for a major city to arise, either. None of the fifteen largest metropolitan areas in the U.S. is situated on any of its fifteen largest rivers by discharge (in fairness, #16 Minneapolis-St. Paul is on the Mississippi). The Nile Valley has not been the richest part of Africa for some time, and the great cities of Brazil are not situated on the banks of the Amazon.
Even in ancient times, urban drinking water needs could be met by transportation (i.e. canals and aqueducts), collection/storage (i.e. reservoirs, cisterns), and groundwater (wells and springs). Jerusalem, which you say lacked an "abundant water supply," used an extensive system of cisterns and reservoirs supplemented by aqueducts to support its population. The same goes for Athens, Byblos, Carthage, Constantinople, and on down the line to Pompeii, Syracuse, and Tyre— given the dry climate and unlacustrine geography of the Mediterranean and Levant, quite a few of its settlements would have relied in groundwater and cisterns, with increasingly longer and more sophisticated aqueducts built, especially starting in the Roman era.
For a more modern example, Dallas, Texas is situated on the Trinity River, but that is a minor waterway that is not navigable. It was founded there for its lack of water— that is to say, a trading post was established at one of the river's few natural fords to service the many wagon trains crossing there. From the trading post grew a metropolitan area of over 6 million residents.
What this illustrates is that a more important driver of growth is trade, and trade is what access to a major river or lake (or the sea or ocean) facilitates. Prior to the invention of the steam engine, transporting goods over land was slow, subject to loss by banditry, and limited by the speed of pack animals. Water was the only feasible medium for shipping cargo in large quantities or over long distances, whether by barge or boat. Communications, too, would have been faster by water, particularly in a mountainous country like Greece, and the presence of a port implies contact with outsiders, contributing to the sharing of ideas. Countries and empires undertook huge canal projects to facilitate water transportation; thousands of miles of them in the United States alone.
Of course, trade is not the sole force behind a city's growth, either. Other population centers became established for political reasons, such as Madrid, or for military reasons, such as Moscow. But in such cases, the availability of water is again secondary. Madrid has a tenuous water supply for a city its size, but had an ideal location for Philip II to establish his court.
The invention of the steam engine, telegraph, and railroad have of course torn all the above considerations apart. Sending a package from New York to San Francisco by clipper ship would have taken three months, half the time to ship it by stagecoach over land. But the transcontinental railroad made it possible to ship it in a week. Such things would have rendered Pheidippides and Andrew Jackson largely invisible to history, but they also made possible cities that would scarcely have thrived otherwise: Los Angeles, watered from hundreds of miles away, is a trade hub because it connects the American railroad network— improbably, over mountains and across deserts— to its busiest port— an artificial harbor dug by steam shovel— and busiest O/D international airport.