In this work, we employ a chemical insights-based diversity-driven approach to search for metal-organic framework (MOF) photocatalysts. With an in silico design based on chemical insights, we populated areas in the chemical design space related to MOFs with photocatalytic potential. We selected a balanced dataset of DFT-based photocatalytic descriptors computed for 314 MOFs, comprising our in silico structures, a diverse subset of the QMOF database, and experimental MOF photocatalysts. With such a balanced dataset, we could fine-tune supervised machine-learning models from literature that allowed us to draw insights into relevant areas in the chemical design space for photocatalysis and potential bottlenecks.Among our in silico MOFs, a few motifs stood out, such as Au-pyrazolate, Ti clusters and rod-shaped metal nodes, and a particular MOF designed with the Mn4Ca cluster, which mimics the OER center in the photosystem II of photosynthesis.Overall, by combining three pillars --- the design of potential MOF photocatalysts guided by chemical insights, the DFT evaluation of photocatalytic descriptors, and the machine-learning approach --- we were able to gain insights into structure-property relationship, and identify trends in the chemical design space that can open new avenues for advancing the field of photocatalysis.