The discovery in 2008 of the iron-based superconducting pnictide and chalcogenide compounds has provided an entirely new family of materials for studying the crucial interplay between superconductivity and magnetism in unconventional superconductors. The alkali-metal-intercalated iron selenide (A_xFe_2−ySe₂, A = alkali metal) superconductors are of particular interest owing to their relatively high transition temperatures over 30 K and the co-existence of the superconducting state with antiferromagnetic ordering. Intrinsic phase separation on the mesoscopic scale is known to occur in 'single crystals' of these compounds, adding to the complexity of interpretation of bulk property measurements. In this study, we investigate the local electronic structure and chemistry of Rb_xFe_2−ySe₂ crystals using scanning microscopy techniques. Nano-focussed angle-resolved photoemission spectroscopy has enabled the band structure of the minority superconducting phase and the non-superconducting matrix to be measured independently and linked to the surface chemistry from the same regions using core level spectroscopy. Valence band mapping reveals the characteristic microstructure of these crystals, but does not have sufficient spatial resolution to enable the precise morphology of the superconducting phase to be elucidated. Cryogenic magnetic force microscopy has shown that the superconducting phase has a fine-scale stripey morphology that was not resolved in the scanning photoemission spectroscopy experiment. The correlation of these findings with previous microstructural studies, bulk measurements and first-principles density functional theory calculations paves the way for understanding the intriguing electronic and magnetic properties of these compounds.