Although severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) initially infects the respiratory tract, it also directly or indirectly affects other organs, including the brain. However, little is known about the relative neurotropism of SARS-CoV-2 variants of concern (VOCs), including Omicron (B.1.1.529), which emerged in November 2021 and has remained the dominant pathogenic lineage since then. To address this gap, we examined the relative ability of Omicron, Beta (B.1.351), and Delta (B.1.617.2) to infect the brain in the context of a functional human immune system by using human angiotensin-converting enzyme 2 (hACE2) knock-in triple-immunodeficient NGC mice with or without reconstitution with human CD34⁺ stem cells. Intranasal inoculation of huCD34⁺-hACE2-NCG mice with Beta and Delta resulted in productive infection of the nasal cavity, lungs, and brain on day 3 post-infection, but Omicron was surprisingly unique in its failure to infect either the nasal tissue or brain. Moreover, the same infection pattern was observed in hACE2-NCG mice, indicating that antiviral immunity was not responsible for the lack of Omicron neurotropism. In independent experiments, we demonstrate that nasal inoculation with Beta or with D614G, an ancestral SARS-CoV-2 with undetectable replication in huCD34⁺-hACE2-NCG mice, resulted in a robust response by human innate immune cells, T cells, and B cells, confirming that exposure to SARS-CoV-2, even without detectable infection, is sufficient to induce an antiviral immune response. Collectively, these results suggest that modeling of the neurologic and immunologic sequelae of SARS-CoV-2 infection requires careful selection of the appropriate SARS-CoV-2 strain in the context of a specific mouse model.