We present HST/NICMOS images at 0.2 resolution of the HI Paschen Alpha (PaA) emission line in a 70 x 90 region of the Galactic center centered on the non-thermal radio source Sgr A*. The majority of the emission arises from ionized gas in the mini-spiral in the central parsec. PaA emission is also seen from 26 stellar sources, presumably early-type stars with mass-loss winds. The new data reveal significant small-scale structure (<1~0.04pc) in the ionized gas of the mini-spiral; low surface brightness emission features are also seen for the first time. Extinction, estimated from the ratio of observed PaA emission to 6-cm continuum emission, varies from 20 to 50 mag with a median Av=31.1 mag, in excellent agreement with earlier estimates for the stellar sources and indepedent measurements derived using H92alpha recombination line data. Large increases in extinction are seen along the periphery of the ionized gas, suggesting that the ionized gas is partially extincted by dust in the molecular clouds at the outside of the ionized regions. The small-scale, filamentary structures in the ionized gas have a free thermal expansion time of only ~ 3000 yrs; either magnetic fields or mass-loss winds from the hot emission line stars may contain the ionized filaments. For both the ionized gas and the stellar continuum, the centroids of the emission remain within ~+/- 1 from a radius of 2 out to 40, providing further evidence that Sgr A* is indeed at or extremely close to the dynamical center of the Galactic nucleus stellar distribution. The 1.9 micron surface brightness increases inwards to 0.9 and then decreases or levels off closer to Sgr A*, possibly indicating the core radius of the central stellar distribution or depletion of the late-type stars by stellar collisions near the central black hole.