We present Space Telescope Imaging Spectrograph observations of 14 nearby low-luminosity active galactic nuclei , including 13 LINERs and 1 Seyfert , taken at multiple parallel slit positions centered on the galaxy nuclei and covering the H \alpha spectral region . For each galaxy , we measure the emission-line velocities , line widths , and strengths , to map out the inner narrow-line region structure , typically within \sim 100 pc from the galaxy nucleus . There is a wide diversity among the velocity fields : in a few galaxies the gas is clearly in disk-like rotation , while in other galaxies the gas kinematics appear chaotic or are dominated by radial flows with multiple velocity components . In most objects , the emission-line surface brightness distribution is very centrally peaked . The [ S ii ] line ratio indicates a radial stratification in gas density , with a sharp increase within the inner 10–20 pc , in the majority of the Type 1 ( broad-lined ) objects . The electron-density gradients of the Type 1 objects exhibit a similar shape that is well fit by a power law of the form \emph { n } _ { \mathrm { e } } = \emph { n } _ { 0 } ( r / 1 ~ { } \mathrm { pc } ) ^ { \alpha } , where \alpha = -0.60 \pm { 0.13 } . We examine how the [ N ii ] \lambda 6583 line width varies as a function of aperture size over a range of spatial scales , extending from scales comparable to the black hole ’ s sphere of influence to scales dominated by the host galaxy ’ s bulge . For most galaxies in the sample , we find that the emission-line velocity dispersion is largest within the black hole ’ s gravitational sphere of influence , and decreases with increasing aperture size toward values similar to the bulge stellar velocity dispersion measured within ground-based apertures . We construct models of gas disks in circular rotation and show that this behavior can be consistent with virial motion , although for some combinations of disk parameters we show that the line width can increase as a function of aperture size , as observed in NGC 3245 . Future dynamical modeling in order to determine black hole masses for a few objects in this sample may be worthwhile , although disorganized motion will limit the accuracy of the mass measurements .