Physical reservoir computing is a computational framework that implements spatiotemporal information processing directly within physical systems. By exciting nonlinear dynamical systems and creating linear models from their state, we can create highly energy-efficient devices capable of solving machine learning tasks without building a modular system consisting of millions of neurons interconnected by synapses. To act as an effective reservoir, the chosen dynamical system must have two desirable properties: nonlinearity and memory. We present task agnostic spatial measures to locally measure both of these properties and exemplify them for a specific physical reservoir based upon magnetic skyrmion textures. In contrast to typical reservoir computing metrics, these metrics can be resolved spatially and in parallel from a single input signal, allowing for efficient parameter search to design efficient and high-performance reservoirs. Additionally, we show the natural trade-off between memory capacity and nonlinearity in our reservoir's behaviour, both locally and globally. Finally, by balancing the memory and nonlinearity in a reservoir, we can improve its performance for specific tasks.