Using the Mopra telescope, we have undertaken a 3-mm spectral-line imaging survey of a 5 arcmin square area around Sgr B2. We covered almost the complete spectral the range from 81.7 to 113.5 GHz, with 2.2 MHz wide spectral channels or 6 km s-1 and have observed 24 lines, with 0.033 MHz wide, or 0.1 km s-1 channels. We discuss the distribution of around 50 lines, and present velocity-integrated emission images for 38 of the lines. In addition, we have detected around 120 more lines, mostly concentrated at the particularly spectral line-rich Sgr B2(N) source. There are significant differences in molecular emission, pointing to both abundance and excitation differences throughout the region. Seven distinct spatial locations are identified for the emitting species, including peaks near the prominent star forming cores of Sgr B2(N), (M) and (S) that are seen in IR-to-radio continuum images. The other features are a 'North Ridge' and a 'North Cloud' to the north of the Sgr B2 N-M-S cores, a 'South-East Peak' and a 'West Ridge'. The column density, as evident through C18O, peaks at the Sgr B2(N) and (M) cores, where strong absorption is also evident in otherwise generally-bright lines such as HCO+, HCN and HNC. Most molecules trace a ridge line to the west of the Sgr B2 N-M-S cores, wrapping around the cores and extending NE to the North Cloud. This is most clearly evident in the species HC_3N, CH_3CN, CH_3OH and OCS. They are found to be closer in distribution to the cooler dust traced by the sub-mm continuum than either the warmer dust seen in the mid-IR or to the radio continuum. The molecule CN, in contrast, is reasonably uniform over the entire region mapped, aside from strong absorption at the positions of the Sgr B2(N) and (M) cores.