Understanding the genomic processes underlying local adaptation is a central aim of modern evolutionary biology. This task requires identifying footprints of local selection but also estimating spatio-temporal variation in population demography and variation in recombination rate and diversity along the genome. Here, we investigated these parameters in blue tit populations inhabiting deciduous versus evergreen forests and insular versus mainland areas, in the context of a previously described strong phenotypic differentiation. Neighboring population pairs of deciduous and evergreen habitats were weakly genetically differentiated (F_ST = 0.004 on average), nevertheless with a statistically significant effect of habitat type on the overall genetic structure. This low differentiation was consistent with the strong and long-lasting gene flow between populations, inferred by demographic modeling. In turn, insular and mainland populations were moderately differentiated (F_ST = 0.08 on average), in line with the inference of moderate ancestral migrations, followed by isolation since the end of the last glaciation. Effective population sizes were overall large, yet smaller on the island than on the mainland. Weak and non-parallel footprints of divergent selection between deciduous and evergreen populations were consistent with their high connectivity and the probable polygenic nature of local adaptation in these habitats. In turn, stronger footprints of divergent selection were identified between long isolated insular versus mainland birds, and were more often found in regions of low recombination as expected from theory. Lastly, we identified a genomic inversion on the mainland, spanning 2.8Mb. These results provide insights into the demographic history and genetic architecture of local adaptation in blue tit populations at multiple geographic scales.