Adaptive evolution requires both raw genetic material and an accessible path of high fitness from one fitness peak to another. In this study, we used an introgression line (IL) population to map quantitative trait loci (QTL) for leaf traits thought to be associated with adaptation to precipitation in wild tomatoes (Solanum sect. Lycopersicon; Solanaceae). A QTL sign test showed that several traits likely evolved under directional natural selection. Leaf traits correlated across species do not share a common genetic basis, consistent with a scenario in which selection maintains trait covariation unconstrained by pleiotropy or linkage disequilibrium. Two large effect QTL for stomatal distribution colocalized with key genes in the stomatal development pathway, suggesting promising candidates for the molecular bases of adaptation in these species. Furthermore, macroevolutionary transitions between vastly different stomatal distributions may not be constrained when such large-effect mutations are available. Finally, genetic correlations between stomatal traits measured in this study and data on carbon isotope discrimination from the same ILs support a functional hypothesis that the distribution of stomata affects the resistance to CO$_2$ diffusion inside the leaf, a trait implicated in climatic adaptation in wild tomatoes. Along with evidence from previous comparative and experimental studies, this analysis indicates that leaf traits are an important component of climatic niche adaptation in wild tomatoes and demonstrates that some trait transitions between species could have involved few, large-effect genetic changes, allowing rapid responses to new environmental conditions.