In urban landscapes, information is required to describe the heterogeneous nature of pedological and hydrological resources. This is particularly the case in areas previously used as municipal landfills. Increasingly, geophysical techniques such as electromagnetic (EM) induction are being used. Here we describe how a single-frequency and multiple-coil EM instrument can be used in conjunction with a one-dimensional spatially constrained quasi-three-dimensional inversion algorithm to map electrical conductivity (σ). The algorithm is briefly described and then applied to soil apparent electrical conductivity (σa) data observed with a DUALEM-421 and across a former municipal landfill at Astrolabe Park in Daceyville, Sydney. The results are presented as isosurface maps of σ. In general, the results compare favorably with existing knowledge and previous research results performed within a highly modified aeolian sand landscape. Specifically, the isosurface maps allow us to discern a gradient in, as well as identify contiguous corridors of, σ, which allow us to infer the likely location of leachate plume flow paths and their origin. The results demonstrate how EM instruments can provide rapid measurements of σa. In addition, coupled to a one-dimensional spatially constrained quasi-three-dimensional inversion algorithm, the data enable robust estimates of σ, which may be useful for informing future natural resource management and research needs in a decommissioned municipal landfill at Astrolabe Park, which is impacted by a leachate plume.