We present scanning tunneling microscopy measurements on a cleaved surface of the recently discovered superconductor NdO$_{0.7}$F$_{0.3}$BiS$_{2}$ with a transition temperature ($T_{mathrm{c}}$) of 5.1 K.Tunneling spectra at 4.2 K (below $T_{mathrm{c}}$) and 22 K (above $T_{mathrm{c}}$) show a large spectroscopic gap ($sim$40 mV), which is inconsistent with the metallic nature demonstrated in bulk measurements. Moreover, we find two interesting real-space electronic features. The first feature is a `checkerboard stripe electronic state characterized by an alternating arrangement of two types of nanocluster. In one cluster, one-dimensional electronic stripes run along one Bi-Bi direction, whereas, in the other cluster, the stripes run along the other Bi-Bi direction. The second feature is a nanoscale electronic inhomogeneity whose microscopic source seems to be atomic defects on the cleaved surface or dopant F atoms.