The Palomar Integral Field Spectrograph was used to probe a variety of environments in nine nearby galaxies that span a range of morphological types, luminosities, metallicities, and infrared-to-blue ratios. For the first time, near-infrared spectroscopy was obtained for nuclear or bright H II regions in star-forming galaxies over two spatial dimensions (57 × 100) in the [Fe II] (1.257 μm), [Fe II] (1.644 μm), Paβ (1.282 μm), H2 (2.122 μm), and Brγ (2.166 μm) transition lines. These data yield constraints on various characteristics of the star-forming episodes in these regions, including their strength, maturity, spatial variability, and extinction. The H II regions stand out from the nuclei. Unlike observations of nuclear regions, H II region near-infrared observations do not show a spatial coincidence of the line and continuum emission; the continuum and line maps of H II regions usually show distinct and sometimes spatially separated morphologies. Gauging from Paβ and Brγ equivalent widths and luminosities, the H II regions have younger episodes of star formation than the nuclei and more intense radiation fields. Near-infrared line ratio diagnostics suggest that H II regions have "purer" starbursting properties. The correlation between ionizing photon density and mid-infrared color is consistent with the star formation activity level being higher for H II regions than for nuclei. And though the interpretation is complicated, on a purely empirical basis the H II regions show lower Fe1+ abundances than nuclei by an order of magnitude.