Aging adults (65+) with disability are especially vulnerable to coronavirus disease 2019 (COVID-19), and on contracting, they are a cohort most likely to require palliative care. Therefore, it is very important that health services—particularly health services providing palliative care—are proximately available. Treating the Melbourne metropolitan area as a case study, a spatial analysis was conducted to clarify priority areas with a significantly high percentage and number of aging adults (65+) with disability and high barriers to accessing primary health services. Afterward, travel times from priority areas to palliative medicine and hospital services were calculated. The geographic dispersion of areas with people vulnerable to COVID-19 with poor access to palliative care and health services is clarified. Unique methods of health service delivery are required to ensure that vulnerable populations in underserviced metropolitan areas receive prompt and adequate care. The spatial methodology used can be implemented in different contexts to support evidence-based COVID-19 and pandemic palliative care service decisions.