Imaging-based spatial transcriptomics technologies such as MERFISH offer snapshots of cellular processes in unprecedented detail, but new analytic tools are needed to realize their full potential. We present InSTAnT, a computational toolkit for extracting molecular relationships from spatial transcriptomics data at the intra-cellular resolution. InSTAnT detects gene pairs and modules with interesting patterns of mutual co-localization within and across cells, using specialized statistical tests and graph mining. We showcase the toolkit on datasets profiling a human cancer cell line and hypothalamic preoptic region of mouse brain. We performed rigorous statistical assessment of discovered co-localization patterns, found supporting evidence from databases and RNA interactions, and identified subcellular domains associated with RNA-colocalization. We identified several novel cell type-specific gene co-localizations in the brain. Intra-cellular spatial patterns discovered by InSTAnT mirror diverse molecular relationships, including RNA interactions and shared sub-cellular localization or function, providing a rich compendium of testable hypotheses regarding molecular functions.