We have obtained HST-NICMOS observations of five of M31's most metal-rich globular clusters: G1, G170, G174, G177, and G280. For the two clusters farthest from the nucleus, G1 and G280, we statistically subtract the field population and estimate metallicities using K-(J-K) color-magnitude diagrams (CMDs). Based on the slopes of their infrared giant branches we estimate [Fe/H]=-1.22+/-0.43 for G1 and -0.15+/-0.37 for G280. We combine our infrared observations of G1 with two epochs of optical HST-WFPC2 V-band data and identify at least one long-period variable (LPV) based on color and variability. The location of G1's giant branch in the K-(V-K) CMD is very similar to that of M107, indicating a somewhat higher metallicity than our purely infrared CMD; [Fe/H]=-0.9+/-0.2. This latter value is more robust, and is supported by the presence of LPVs. For the field surrounding G280, we estimate the metallicity to be -0.3 from the slope of the giant branch, with a spread of σ[Fe/H]~0.4 based on the width of the giant branch. For the three central clusters, which are too compact for accurate cluster star measurements, we present integrated cluster magnitudes and CMDs for the surrounding fields. The K-band luminosity functions (LFs) of the upper few magnitudes of G1 and G280, as well as for the fields surrounding all of the clusters, are indistinguishable from the LF measured in the bulge of our Galaxy. This indicates that these clusters are very similar to Galactic globular clusters, and, at least in the surrounding fields observed, there are no significant populations of young luminous stars. Based on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy (AURA), Inc., for NASA under contract NAS 5-26555.