We describe theoretically the structure and properties of layered lead organohalide perovskites, considering purely bi-dimensional (2D) PbI4 layers, and quasi-2D systems where the inorganic layers are formed by more than one lead iodide sheet. The intercalating organic dications were designed to have low lying virtual orbitals (LUMO), so as to induce in the perovskite the appearance of virtual bands, localized in the organic layer, either close to the inorganic conduction band bottom or valence band top, or in some cases in the middle of the inorganic band gap. Such a feature is quite uncommon for this class of materials, and deserves attention since it allows one to tune the effective band gap of the material, possibly leading to the absorption of visible light and influencing the optical properties deeply. We discuss the effect of functional groups on the organic cations, and of the different symmetries used in geometry optimizations: a careful analysis of the contributions to the dispersion curves and band gaps was performed. The charge carrier mobility is also discussed, computing the conductivity over relaxation time and the effective masses for all the systems, with particular attention to the features related to the unusual organic intra-gap bands. All the structures were optimized at the DFT level, with inclusion of dispersion effects; dispersion curves were computed with full relativistic potentials, and the band gaps corrected for long range coulombic effects at the GW level. A semiempirical approach, based on the integration of charge carrier group velocities over a dense grid of k-points, was used to compute the conductivities and effective masses.