Electrically conducting 2D metal-organic frameworks (MOFs) have attracted considerable interest, as their hexagonal 2D lattices mimic graphite and other 2D van der Waals stacked materials. However, understanding their intrinsic properties remains a challenge because their crystals are too small or of too poor quality for crystal structure determination. Here, we report atomically precise structures of a family of 2D pi-conjugated MOFs derived from large single crystals of sizes up to 200 mu m, allowing atomic-resolution analysis by a battery of high-resolution diffraction techniques. A designed ligand core rebalances the in-plane and out-of-plane interactions that define anisotropic crystal growth. We report two crystal structure types exhibiting analogous 2D honeycomb-like sheets but distinct packing modes and pore contents. Single-crystal electrical transport measurements distinctively demonstrate anisotropic transport normal and parallel to the pi-conjugated sheets, revealing a clear correlation between absolute conductivity and the nature of the metal cation and 2D sheet packing motif. Two-dimensional MOFs can possess porosity and electrical conductivity but are difficult to grow as single crystals. Here, by balancing in-plane and out-of-plane interactions, single crystals of sizes up to 200 mu m are grown, allowing in-plane transport measurements and atomic-resolution analysis.