Spontaneous neural dynamics manifest in periodic and aperiodic activity, which are hierarchically organized and intrinsic to different brain areas, in a way thought to mediate information processing of environmental stimuli during wake. Particularly prominent are intrinsic neural timescales, a measure of temporal autocorrelation, which reflect functional significance for cognition, changes in gene expression, and modulations in brain disorders. To date, however, less is known about the regional distribution of neural timescales at the whole-brain level during sleep in humans, where the need for external stimuli processing is diminished. Here, we aimed at characterizing the changes of neural timescales from wake to NREM3 and REM sleep across a widespread cortical hierarchy. To this aim, we leveraged the MNI Open iEEG Atlas (N=106 patient, n=1772 electrodes in wake) and computed intrinsic timescales across wake and sleep. Consistent with recent studies, timescales in NREM3 sleep are higher in all areas, with parietal and prefrontal areas showing the highest increase and the medial temporal lobe the least. We observed a general increase also in REM sleep, although less than NREM3, with a particularly prominent increase in sensory and medial temporal lobe areas. Importantly, timescales follow the sensory-association axis during wake and NREM3, as indexed by a negative correlation with the T1w/T2w ratio of myelin content, but not REM sleep. Our results suggest that timescales in wakefulness are shaped both by anatomy and microstructure as previously reported, and that this relation is not static but is instead modulated by the sleep/wake cycle.