To narrow the scope, let's keep this to the Mediterranean/Near East, but if someone can speak about how this played out in India/China, that'd be awesome too!
I'll chip in on Mesopotamia: if you're asking about brand new cities specifically (i.e. large-scale urban planning from scratch, instead of smaller settlements like forts and satellite villages around growing cities), it didn't occur very often at all. In Iron Age II we have a couple of high-profile examples (Kalhu/Nimrud and Dur Sharruken), but in the Bronze Age virtually all new settlements were either too small to be called cities, or were founded on previously inhabited sites.
A major contributing factor to this is the basic fact of geography: Mesopotamia is an alluvial plain. Because of this it doesn't have many natural hills, and hills naturally attract habitation because they are easily defensible. However, any place that did get settled (and subsequently abandoned and again resettled) became an artificial mound, called a tell, over time. Because they became hills over time, tells became the logical place to settle - after all, why build on the plain if you could build on the hill?
Recommended reading: Wilkinson (2003), Archaeological Landscapes of the Near East, University of Arizona Press (particularly chapter 6, 'Landscapes of Tells', which focuses on the Bronze Age).