The success of a mobile edge computing network depends critically on how to assign the edge servers to the user cells. The criterion for this assignment is application-specific. In many practical applications, the workload demanded by each cell is unknown and time-varying. So are the effective capacities of the servers. We need an assignment incurring minimum backhaul cost that is robust to these uncertainties. We also want to make the cells assigned to the same server form a geographically compact cluster. This challenge motivates us to introduce a novel stochastic geo-aware partitioning problem. As it is computationally hard, we propose a heuristic algorithm that can produce a range of solutions representing different tradeoffs between cost minimization versus geographical awareness. We evaluate the proposed algorithm using a real-world dataset.