We present nulling interferometric observations of six nearby main-sequence stars (α CrB, α Lyr, β Leo, γ Ser, epsilon Eri, and ζ Lep). None of the stars show evidence for a positive detection of warm debris in the habitable zone of the systems. Using a scaled up model of solar zodiacal emission, the 3σ upper limits on dust density range from 220 to 104 Zody (1 Zody = the density of our own solar zodiacal cloud) depending on the particular star, corresponding to mass limits of 10-7 to 10-5 M ⊕ of micron-sized dust. These limits contrast with the presence of dust at greater separations from the star, implying a clearing in dust in the inner system. This suggests that the inner circumstellar environment around nearby intermediate-mass main-sequence stars more than several tens of millions of years old are generally cleared of dusty debris. Finally, the well studied nature of the debris disks around Vega, epsilon Eridani, and ζ Leporis allows us to place these 10 μm nulling observations in the context of previous studies to determine the physical processes responsible for shaping the debris disk in these particular systems.The results presented here made use of the MMT Observatory, a jointly operated facility of the University of Arizona and the Smithsonian Institution.