(Abridged) We present STIS 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. 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. 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 objects. We examine how the [N II] 6583 line width varies as a function of aperture size over a range of spatial scales, extending from scales comparable to the black holes sphere of influence to scales dominated by the host galaxys bulge. For most galaxies in the sample, we find that the emission-line velocity dispersion is largest within the black holes gravitational sphere of influence, and decreases with increasing aperture size toward values similar to the bulge stellar velocity dispersion measured within ground-based apertures. 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.
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