We present arcsecond-scale observations of the active galactic nuclei (AGNs) of seven nearby Seyfert galaxies observed from the Stratospheric Observatory For Infrared Astronomy (SOFIA) using the 31.5 and 37.1 μm filters of the Faint Object infraRed CAmera for the SOFIA Telescope (FORCAST). We isolate unresolved emission from the torus and find extended diffuse emission in six 37.1 μm residual images in our sample. Using Spitzer/IRS spectra, we determine the dominant mid-infrared (MIR) extended emission source and attribute it to dust in the narrow-line region (NLR) or star formation. We compare the optical NLR and radio jet axes to the extended 37.1 μm emission and find coincident axes for three sources. For those AGNs with extended emission coincident with the optical axis, we find that spatial scales of the residual images are consistent with 0.1-1 kpc scale distances to which dust can be heated by the AGN. Using previously published subarcsecond 1-20 μm imaging and spectroscopic data along with our new observations, we construct broad-band spectral energy distributions (SEDs) of the AGNs at wavelengths 1-40 μm. We find that three AGNs in our sample tentatively show a turnover in the SED between 30 and 40 μm. Using results from CLUMPY torus models and the Bayesian inference tool BAYESCLUMPY, we find that the posterior outputs for AGNs with MIR turnover revealed by SOFIA/FORCAST have smaller uncertainties than AGNs that do not show a turnover.