We develop a location-based coarse-graining method for characterizing solvent density inhomogeneities and use it to investigate a two-dimensional supercritical Lennard-Jones fluid. The strength of this method is that it treats any high-and low-density domains present in the fluid equivalently, rather than focusing on the high-density "clusters" alone. As the critical region is approached, we find that the distribution of local densities found in this fluid becomes quite broad, while, more globally, the high- and low-density domain structure changes from singly continuous to bicontinuous. Concurrently, these domains grow in size, as expected from the divergence of the correlation length; yet, we find that the correlation length is a very poor indicator of this change, greatly underestimating the length of large domains. This result is in part due to the very asymmetric topology of the domains, which, we find, is relatively invariant to changes in thermodynamic conditions or to the proximity of the critical point.