Hybrid organic-inorganic halide perovskites are under intense investigations because of their astounding physical properties and promises for optoelectronics. Lead bromide and chloride perovskites exhibit intrinsic white-light emission believed to arise from self-trapped excitons (STEs). Here, we report a series of new structurally diverse hybrid lead bromide perovskites that have broad-band emission at room temperature. They feature Pb/Br structures which vary from 1D face-sharing structures to 3D corner- and edge-sharing structures. Through single-crystal X-ray diffraction and low-frequency Raman spectroscopy, we have identified the local distortion level of the octahedral environments of Pb within the structures. The band gaps of these compounds range from 2.92 to 3.50 eV, following the trend of "corner-sharing < edge-sharing < face-sharing". Density functional theory calculations suggest that the electronic structure is highly dependent on the connectivity mode of the PbBr octahedra, where the edge- and corner-sharing 1D structure of (2,6-dmpz)PbBr exhibits more disperse bands and smaller band gap (2.49 eV) than the face-sharing 1D structure of (hep)PbBr (3.10 eV). Using photoemission spectroscopy, we measured the energies of the valence band of these compounds and found them to remain almost constant, while the energy of conduction bands varies. Temperature-dependent PL measurements reveal that the 2D and 3D compounds have narrower PL emission at low temperature (∼5 K), whereas the 1D compounds have both free exciton emission and STE emission. The 1D compound (2,6-dmpz)PbBr has the highest photoluminescence quantum yield of 12%, owing to its unique structure that allows efficient charge carrier relaxation and light emission.