We combine Hα imaging with the CO-line observations of the Five College Radio Astronomy Observatory Extragalactic CO Survey to study the relationship between molecular gas and high-mass star formation for 568 regions in 121 galaxies at 45" resolution. Our study finds a strong correlation between these quantities when sampled locally within galaxies, consistent with recent studies of globally averaged quantities. For spiral galaxies, there are no strong radial gradients in the star formation efficiency across the star-forming disk, although star formation efficiencies measured in the outermost regions (R>9 kpc) of midsized galaxies tend to be systematically low. Additionally, star formation efficiencies in large (D0>60 kpc) galaxies are uniformly low at all radii compared with smaller galaxies. As a function of morphology and environment, the behavior of the star formation efficiency within galaxies is consistent with the results of our previous investigation of the global quantities. Among spirals the star formation efficiency does not depend on Hubble type, with a similar range of efficiencies within each type and less than 25% variation in the mean from type to type. Finally, relative to an isolated galaxy sample, the star formation efficiency is found to be sensitive only to extreme variations in the galaxy environment. The star formation efficiency decreases steadily with increasing H I deficiency among Virgo cluster spirals, and it is enhanced in strong interactions and mergers.