Characterization of cell type specific regulatory networks and elements is a major challenge in genomics, and emerging strategies frequently employ high-throughput genome-wide assays of transcription factor (TF) to DNA binding, histone modifications or chromatin state. However, these experiments remain too difficult/expensive for many laboratories to apply comprehensively to their system of interest. Here, we explore the potential of elucidating regulatory systems in varied cell types using computational techniques that rely on only data of gene expression, low-resolution chromatin accessibility, and TF-DNA binding specificities ('motifs'). We show that static computational motif scans overlaid with chromatin accessibility data reasonably approximate experimentally measured TF-DNA binding. We demonstrate that predicted binding profiles and expression patterns of hundreds of TFs are sufficient to identify major regulators of ∼200 spatiotemporal expression domains in the Drosophila embryo. We are then able to learn reliable statistical models of enhancer activity for over 70 expression domains and apply those models to annotate domain specific enhancers genome-wide. Throughout this work, we apply our motif and accessibility based approach to comprehensively characterize the regulatory network of fruitfly embryonic development and show that the accuracy of our computational method compares favorably to approaches that rely on data from many experimental assays.