Geostatistical tools are considered to be very imperative in achieving the Sustainable Development Goals (SDGs), most especially in the distribution of facilities. Studies on the application of geostatistics such as Average Nearest Neighbour (ANN) in the spatial distribution of sustainable water supply facilities are often very rare. This study, therefore, explores the critical importance of the ANN analytical tool of ArcGIS to examine the spatial distribution of public water supply facilities in Lapai, Nigeria. The ANN sets the null hypothesis that there is no difference between the random distribution and the distribution of public water facilities in the study area, where the z-score and p-value results are both measures of statistical significance which explains whether the null hypothesis should be accepted or rejected. The results obtained indicate a similar spatial distribution pattern for all water facilities in the study area, as they are dispersedly distributed from the global view. The method will allow more proactive decision making in the provision of sustainable public water supply facilities to better the wellbeing of urban dwellers.