We consider theoretically a network of directly coupled optical microcavities to implement a space-multiplexed optical neural network in an integrated nanophotonic circuit. Nonlinear photonic network integrations based on direct coupling ensures a highly dense integration, reducing the chip footprint by several orders of magnitude compared to other implementations. Different nonlinear effects inherent to such microcavities are studied when used for realizing an all-optical autonomous computing substrate, here based on the reservoir computing concept. We provide an in-depth analysis of the impact of basic microcavity parameters on computational metrics of the system, namely, the dimensionality and the consistency. Importantly, we find that differences between frequencies and bandwidths of supermodes formed by the direct coupling is the determining factor of the reservoir's dimensionality and its scalability. The network's dimensionality can be improved with frequency-shifting nonlinear effects such as the Kerr effect, while two-photon absorption has an opposite effect. Finally, we demonstrate in simulation that the proposed reservoir is capable of solving the Mackey-Glass prediction and the optical signal recovery tasks at GHz timescale.