I know that Ur at its height had a population between 50,000 and 80,000 (or was it Uruk?), but what would the population of the lands outside the city have been? Were there satellite villages and towns outside of these cities? Throughout history, the majority of the population has been rural. Did this apply to Mesopotamia?
Firstly I can only really speak for the Ubaid and Uruk periods of Mesopotamian history which predate any of the Mesopotamian empires. Secondly ancient demography is an incredibly difficult task and due to the sheer amount of the time that separates us and the Ubaid and Uruk periods it makes the estimation of the populations very difficult. For reference the Ubaid period runs from 6500-4000 BCE and the Uruk period runs from around 4000-3000 BCE.
During this vast period of 3500 years we see the beginnings of urbanization. The late Ubaid saw a rapid growth in urban areas that is linked to a significant expansion of irrigation throughout the region. This process of urbanization continued through the Uruk period through the abandonment of rural settlements in favor of urban, that is towns of 10+ ha or cities of 40+ ha, sites.
During the Ubaid the majority of the population will have been rural, though as the period progressed a greater and greater number of peoples gravitated towards urban sites and it is estimated that by the early Uruk some 40% of the Uruk/Warka region's population was urban in nature. By the middle Uruk and late Uruk periods the population of the Uruk/Warka region may have been 60% urban and perhaps up to 70% of the population of the Nippur-Adab region was urban. This would increase in the Early Dynastic period to some 80% of the population living in sites greater than 10 ha which were generally clustered fairly close together.
Apart from the this largely urban population there was most probably a significant nomadic population though it's population is not really possible to estimate as there is almost no material evidence for their presence but given their appearance in literary sources we can assume that they were a prominent part of the regions population through the late Uruk and Early Dynastic periods and presumably the Ubaid period as well.
Now as to the actual population of Sumer in these periods I'm afraid I haven't actually come across many estimates of the total population of the region but looking at the number of small and large urban sites I suppose we could estimate it in the high hundreds of thousands to perhaps a million.
Ancient Mesopotamia, Susan Pollock, 1999
Ancient Mesopotamia at the Dawn of Civilization: The Evolution of an Urban Landscape, Guillermo Algaze, 2008