The inner edge of the classical habitable zone is often defined by the critical flux needed to trigger the runaway greenhouse instability. This 1D notion of a critical flux, however, may not be so relevant for inhomogeneously irradiated planets, or when the water content is limited (land planets). Here, based on results from our 3D global climate model, we find that the circulation pattern can shift from super-rotation to stellar/anti stellar circulation when the equatorial Rossby deformation radius significantly exceeds the planetary radius. Using analytical and numerical arguments, we also demonstrate the presence of systematic biases between mean surface temperatures or temperature profiles predicted from either 1D or 3D simulations. Including a complete modeling of the water cycle, we further demonstrate that for land planets closer than the inner edge of the classical habitable zone, two stable climate regimes can exist. One is the classical runaway state, and the other is a collapsed state where water is captured in permanent cold traps. We identify this "moist" bistability as the result of a competition between the greenhouse effect of water vapor and its condensation. We also present synthetic spectra showing the observable signature of these two states. Taking the example of two prototype planets in this regime, namely Gl581c and HD85512b, we argue that they could accumulate a significant amount of water ice at their surface. If such a thick ice cap is present, gravity driven ice flows and geothermal flux should come into play to produce long-lived liquid water at the edge and/or bottom of the ice cap. Consequently, the habitability of planets at smaller orbital distance than the inner edge of the classical habitable zone cannot be ruled out. Transiting planets in this regime represent promising targets for upcoming observatories like EChO and JWST.