We use mid-infrared spectroscopy of unobscured active galactic nuclei (AGNs) to reveal their native dusty environments. We concentrate on Seyfert 1 galaxies, observing a sample of 31 with the Infrared Spectrograph aboard the Spitzer Space Telescope, and compare them with 21 higher-luminosity quasar counterparts. Silicate dust reprocessing dominates the mid-infrared spectra, and we generally measure the 10 and 18 micron spectral features weakly in emission in these galaxies. The strengths of the two silicate features together are sensitive to the dust distribution. We present numerical radiative transfer calculations that distinguish between clumpy and smooth geometries, which are applicable to any central heating source, including stars as well as AGNs. In the observations, we detect the obscuring ``torus'' of unified AGN schemes, modeling it as compact and clumpy. We also determine that star formation increases with AGN luminosity, although the proportion of the galaxies' bolometric luminosity attributable to stars decreases with AGN luminosity.