Wireless networks at millimeter wavelengths have significant implementation difficulties. The path loss at these frequencies naturally leads us to consider antenna arrays with many elements. In these arrays, local oscillator (LO) generation is particularly challenging since the LO specifications affect the system architecture, signal processing design, and circuit implementation. We thoroughly analyze the effect of LO architecture design choices on the performance of a mm-wave massive MIMO uplink. This investigation focuses on the tradeoffs involved in centralized and distributed LO generation, correlated and uncorrelated phase noise sources, and the bandwidths of PLLs and carrier recovery loops. We show that, from both a performance and implementation complexity standpoint, the optimal LO architecture uses several distributed subarrays locked to a single intermediate-frequency reference in the low GHz range. Additionally, we show that the choice of PLL and carrier recovery loop bandwidths strongly affects the performance; for typical system parameters, loop bandwidths on the order of tens of MHz achieve SINRs suitable for high-order constellations. Finally, we present system simulations incorporating a complete model of the LO generation system and consider the case of a 128-element array with 16x-spatial multiplexing and a 2 GHz channel bandwidth at 75 GHz carrier. Using our optimization procedure we show that the system can support 16-way spatial multiplexing with 64-QAM modulation.