I would envisage a solution which would be based on the (hopefully) evolving values of the general human population, after the abolishment of currency. By this I mean that after currency is abolished, there may well be a paradigm shift in peoples concepts of 'value', as people start to move away from the current exchange based way of thinking, and into a more generous mindset.
This will mean that in society, the people will the most perceived 'value' will be those who are most generous, or who give the most, in contrast to todays society (generally speaking), where the more material possessions one acquires, the more perceived value that individual is attributed by the general population.
Building on this prediction, I would suggest that a good way to perpetuate a more 'giving' values system, and solve the problem of how to decide where people would live, would be to reward those who give the most. One way this system could do so, would be to allow the most giving individuals to have first pick of the places they wanted to live, almost like a system of 'altruistic credit'. This system could be managed autonomously by a de-centralised technology platform, to ensure transparency and equality.