  (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 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.
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.
