One major question in galaxy evolution is where the energy from supermassive black holes at the centers of galaxies comes from and how it couples to the surrounding medium. We seek to understand how feedback might work by investigating the X-ray properties of early-type galaxies with radio sources and with and without multiphase gas. Chandra observations of NGC 4261 revealed unusually low entropy inside the central ~kpc of the galaxy, which hosts an extraordinarily powerful radio source (2.29×1024 W/Hz in the 1.4 GHz band). We analyzed Chandra archival observations of twelve additional early-type galaxies with powerful radio sources. We find that IC4296 also has unusually low entropy inside ~1 kpc. Cold clouds may be precipitating out of the hot ambient medium in only that central region and providing fuel for accretion. NGC 4261 and IC4296 may represent an important phase during which powerful feedback from a central AGN is fueled by rapid multiphase gas condensation in the central kpc of the galaxy; but this phase may be short-lived as the AGN jets pump energy into the outer regions and increase the entropy and cooling time of its large-scale gas reservoir. We also investigated the gas properties in the Chandra archival sample of 49 early-type galaxies from Lakhchaura+2018. We consider the relationship between entropy profile slope, multiphase gas extent, ratio between cooling time and free-fall time, and stellar velocity dispersion simultaneously to look for potential correlations. We examine sub-samples restricted by data quality and gas properties and compare the correlations to expectations from theoretical models.