Access to resources and services needs to be considered from a multi-dimensional perspective to capture the complex landscape of human experience. The robust body of research exploring food access has multiple limitations that create an incomplete view of food access, like studies limited to only one mode of transit and inconsistent methods across studies which limit generalizability. This study proposes a framework to formulate a multi-dimensional access index that considers travel time, operating hours, and availability of transit infrastructure across space. We use food pantries in New York City as a case study since there are relatively few of them and they have limited opening hours. We propose an index that quantifies spatiotemporal access by different modes of transportation and takes operating hours of food pantries into account during a one week time period. We compare our results to two traditional access measures and demonstrate that our index provides a significantly different measure of access. We utilize this index to highlight areas of high need but low resources, which shows the importance of this tool to policy makers and service providers. We use our experience of developing this index to highlight the challenges with quantitative analysis of human experience. Our tool is reproducible through an open-access software, which allows researchers and policy-makers to utilize it with parameters that reflect their communities.