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This paper discusses a paradigm we refer to as neurobiomimetic, which involves emulations of brain neuroanatomy and neurobiology aspects and processes. Neurobiomimetic constructs include rudimentary and down-scaled computational representations of brain regions, sub-regions, and synaptic connectivity. Many different instances of neurobiomimetic constructs are possible, depending on various aspects such as the initial conditions of synaptic connectivity, number of neuron elements in regions, connectivity specifics, and more, and we refer to these instances as 'animats'. While downscaled for computational feasibility, the animats are very large constructs; the animats implemented in this work contain over 47,000 neuron elements and over 720,000 synaptic connections. The paper outlines aspects of the animats implemented, spatial memory and learning cognitive task, the virtual-reality environment constructed to study the animat performing that task, and discussion of results. In a broad sense, we argue that the neurobiomimetic paradigm pursued in this work constitutes a particularly promising path to artificial cognition and intelligent unmanned systems. Biological brains readily cope with challenges of real-life tasks that consistently prove beyond even the most sophisticated algorithmic approaches known. At the cross-over point of neuroscience, cognitive science and computer science, paradigms such as the one pursued in this work aim to mimic the mechanisms of biological brains and as such, we argue, may lead to machines with abilities closer to those of biological species.