Moscow was build on a small river. It is in the 20th Cent. when through a channel Volga waters poured into Moskva river and it became... hmmm... a medium river.
Rome was built on Tiber - even smaller river.
Maya cities were built on marshes.
Really, old capital cities, especially in Europe, were rather small towns in nowadays terms and even a small river was enough at start. And later they simply transported the fresh water, if needed. Often by water, as in old Moscow or Venice.
A city needed rather a strong agricultural area around - the food was more serious problem.
And in the East they used some alternative methods to get the water. Karez water systems, or simply covering all valleys and mini-valleys bottoms by flat stones. The water condenses on the stones at night, gets below, cannot be evaporated during the day due to the covering and pours safely along the valley.
In the end of 18th century in Kafa there lived more than 150000 people using this atmospheric water by hand made brooks. After Russia got Crimea, the stones were taken for buildings and brooks disappeared. And the same town Feodosia in the end of 20 century had only 75000 inhabitants taking the water from the Dnepr by a huge channel.
So, using green technologies, you needn't a river. And without them, any river is not enough.