We explore brane induced gravity on a 3-brane in six locally flat dimensions. To regulate the short distance singularities in the brane core, we resolve the thin brane by a cylindrical 4-brane, with the geometry of 4D Minkowski $\times$ a circle, which has an axion flux to cancel the vacuum pressure in the compact direction. We discover a large diversity of possible solutions controlled by the axion flux, as governed by its boundary conditions. Hence brane induced gravity models really give rise to a landscape of vacua, at least semiclassically. The vacuum energy problem is different in brane induced gravity: instead of tuning the 4D curvature, generically one must tune the crossover scale. The most interesting case is the near-critical limit, branes live inside very deep throats which efficiently compactify the angular dimension. In there, 4D gravity first changes to $5D$, and only later to $6D$. The crossover scale saturates at the gravitational see-saw scale, independent of the tension, but the $5D$ to $6D$ transition is still sensitive to it. Using the fields of static loops on a wrapped brane, we check the perturbative description of long range gravity below the crossover scale. Near the critical limit, linearized perturbation theory remains under control below the crossover scale, and we find that linearized gravity around the vacuum looks like a scalar-tensor theory.