Physical and chemical properties of the interstellar medium (ISM) at sub-galactic ($sim$kpc) scales play an indispensable role in controlling the ability of gas to form stars. As part of the SMAUG (Simulating Multiscale Astrophysics to Understand Galaxies) project, in this paper, we use the TNG50 cosmological simulation to explore the physical parameter space of 8 resolved ISM properties in star-forming regions to constrain the areas of this hyperspace over which most star-forming environments exist. We deconstruct our simulated galaxies spanning a wide range of mass (M$_star = 10^{7-11}$ M$_odot$) and redshift ($0 leq z leq 3$) into kpc-sized regions, and statistically analyze the gas/stellar surface densities, gas metallicity, vertical stellar velocity dispersion, epicyclic frequency and dark-matter volumetric density representative of each region in the context of their star formation activity and galactic environment (radial galactocentric location). By examining the star formation rate (SFR) weighted distributions of these properties, we show that stars primarily form in two spatially distinct environmental regimes, which are brought about by an underlying bi-component radial SFR surface density profile in galaxies. We examine how the relative prominence of these two regimes depends on host galaxy mass and cosmic time. We also compare our findings with those from integral field spectroscopy observations and achieve a good overall agreement. Further, using dimensionality reduction, we characterise the aforementioned hyperspace to reveal a high-degree of multicollinearity in relationships amongst ISM properties that drive the distribution of star formation at kpc-scales. Based on this, we show that a reduced 3D representation underpinned by a multi-variate radius relationship is sufficient to capture most of the variance in the original 8D space.
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