I recently spent some time in Jordan and it is amazing what the Nabateans, Greeks, Romans, and other peoples did to manage water thousands of years ago. They were redirecting water over long distances and getting it up mountains in ancient times without magic or fantastical beasts.
Petra is especially amazing. Far smaller than Waterdeep, it had 20,000 to 30,000 inhabitants at its peak, but still it supported that many people, situated in a region with limited water resources. They used a system of dams, elaborate channels and pipes, and cisterns to capture and store rainwater. They also constructed several large dams in the vicinity to capture the occasional flash flood that happened in the area. The dams would slow down the flow of water, allow sediment to settle, enabling collection of clean water in downstream reservoirs.
Further, they had an intricate network of water conduits and and aqueducts they used to transport water from distant springs.
No rivers. No lakes. Supported up to 30,000 people with drinking water, water for agriculture on terraced gardens, and water for the locals animals and the animals of the caravans.
Also, no waterways for moving goods. All by road, on caravans. Yet it was a major trading hub in the ancient world. They were importing massive stone columns and statuary from Egypt, Greece, and Rome...by road.
EDIT
Also look at Aman (Philadelphia in Roman times). It was not located near any large rivers, though there were smaller seasonal streams and wadis (dry river beds that are dry most of the year but carry water during the rainy season). The nearest major river, the river Jordan, is several dozen kilometers away from the city. It relied on underground wells, reservoirs, and transporting water over long distances from other regions through pipelines and aqueducts.
One primary source of water for the city was Ain Ghazl springs, 11 kilometers (7 miles) away. Another was the Qanatir Aquaduct, which brought water from the Wadi al-Seraj area, around 20 kilometers away (12 miles).
Now these are much smaller populations than Waterdeep.
But lets look at Carthage. It is estimated to have had over 100,000 people and, while near the sea, had no nearby river or lake for its water supply. They relied on collecting rainwater, wells, nearby natural springs, and cistrens carved in bedrock under the city. They also constructed systems of aquaducts to bring water from distant areas. The Zaghouan Aquaduct brought water from the Zaghouan mountains, 70 KM (43 miles) away.
And, finally, they imported water through maritime trade.
A city like Waterdeep, which has much higher year-round precipitation, with Renaissance-like technology, fresh underground water sources--right under the city--and magic could certainly provide sufficient water for its population if Carthage could do it.