Higher brain regions are thought to use the computational advantages of sitting closer to a critical point to support more complex cognitive functions. Finding evidence for this hypothesis from neural data is challenging, requiring robust and accurate measures of the distance to criticality (DTC). Many existing metrics of criticality---such as increased signal variance and slower timescales---are derived from analytically tractable systems with fixed or low-amplitude dynamical noise. However, the brain is highly stochastic, with noise levels that can vary between regions, recordings, or individuals, and cause conventional metrics to fail. Here, we took a novel, data-driven approach to the problem of inferring the DTC in the presence of unknown noise. We surveyed a vast library of over 7000 time-series features, evaluated on simulated near-critical systems, to uncover algorithms that are highly informative of the DTC but insensitive to the noise level. We then scrutinized these noise-robust algorithms to develop new theoretical insights, before summarizing our understanding into a practical feature for inferring the DTC in noisy real-world systems: the rescaled auto-density (RAD). Equipped with RAD, we used open electrophysiological data (`Allen Visual Behavior---Neuropixels’) to investigate how the DTC varies across six regions of the visual cortical hierarchy. We found that RAD robustly increases with hierarchical rank (median $\tau=0.55, p<10^{-18}$, across individuals; group-level $\tau=0.42, p<10^{-6}$), whereas conventional metrics of the DTC---standard deviation and autocorrelation---both had non-significant correlations. This finding suggests that higher visual areas are positioned closer to criticality, even though they may be influenced by varied levels of noise or stochastic input. Moreover, our new feature, RAD, is a viable tool for other problems involving critical phenomena, such as seizure prediction or ecological monitoring, and our data-driven methodology demonstrates the potential for large-scale algorithmic comparison to generate new theory along with practical, interpretable tools.