We consider variants of the Jaynes-Cummings-Hubbard model of lattice polaritons, taking into account next-nearest-neighbor, diagonal and long-range photon hopping in one and two dimensions. These models are relevant for potential experimental realizations of polariton Mott insulators based on trapped ions or microwave stripline resonators. We obtain the Mott-superfluid phase boundary and calculate excitation spectra in the Mott phase using numerical and analytical methods. Including the additional hopping terms leads to a larger Mott phase in the case of trapped ions, and to a smaller Mott phase in the case of stripline resonators, compared to the original model with nearest-neighbor hopping only. The critical hopping for the transition changes by up to about 50 percent in one dimension, and by up to about 20 percent in two dimensions. In contrast, the excitation spectra remain largely unaffected.
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