Increasingly frequent marine heatwaves devastate coral reefs around the world, so there is great interest in finding warm-adapted coral populations that could be used as sources for assisted gene flow and restoration. Here, we evaluated the relative power of various environmental factors to explain coral genetic variation, suggestive of differential local adaptation to these factors, across the Florida Keys Reef Tract. We applied a machine learning population genomic method (RDAforest) to two coral species - the mustard hill coral Porites astreoides and the lettuce coral Agaricia agaricites - sampled from 65 sites covering the whole reef tract. Both species comprised three genetically distinct lineages distributed across depths in a remarkably similar way. Within these lineages, there was additional genetic variation explained by depth, but even more within-lineage variation was cumulatively explained by water chemistry parameters related to nitrogen, phosphorus, silicate, and salinity. Visualizing the predicted environment-associated genetic variation on a geographic map suggests that these associations reflect adaptation to certain aspects of the inshore-offshore environmental gradient, and, to a lesser extent, to difference of Middle and Lower Keys from the rest of the reef tract. Thermal parameters, most notably maximal monthly thermal anomaly, were also consistently identified as putative drivers of genetic divergence, but had a relatively low explanatory power compared to depth and water chemistry. Overall, our results indicate that temperature is not the most important driver of differential coral adaptation in the Florida Keys, and underscore depth and water chemistry as more important environmental factors from the corals\' perspective. These findings are relevant for planning assisted gene flow and restoration efforts: not just any warmer reef would be an optimal source of transplants to promote thermal adaptation within the local coral population.