We measured high spatial/depth resolution 300 K thermal conductivity κ of the Zn and O surfaces of two bulk n-type ZnO (0001) samples, grown by a vapor-phase transport method, using scanning thermal microscopy (SThM). The thermal investigation was performed in both point-by-point (∼2 μm resolution) and area-scan modes. On the first sample κ=1.16±0.08 (Zn face)/1.10±0.09 (O face) W/cm K while for the second material κ=1.02±0.07 (Zn face)/0.98±0.08 (O face) W/cm K. These are the highest κ values reported on ZnO. A correlation between SThM area-scan readings and surface topography was established by simultaneously performing atomic force microscopy scans. The influence of surface roughness on the effective thermal conductivity (i.e., heat flow) is discussed.