Using an extensive sample of nearby galaxies (the Nearby Galaxies Catalog, by Tully), we investigate the environment of the galaxies hosting low-luminosity active galactic nuclei (AGNs) (Seyfert galaxies and low-ionization nuclear emission-line regions [LINERs]). We define the local galaxy density, adopting a new correction for the incompleteness of the galaxy sample at large distances. We consider both a complete sample of bright and nearby AGNs, identified from the nuclear spectra obtained in available wide optical spectroscopic surveys, and a complete sample of nearby Seyfert galaxies. Basically, we compare the local galaxy density distributions of the AGNs with those of non-AGN samples, chosen in order to match the magnitude and morphological type distributions of the AGN samples. We find, only for the early-type spirals more luminous than similar to M*, that both LINERs and Seyfert galaxies tend to reside in denser environments on all the scales tested, from tenths of Mpc to a few Mpc; moreover Seyfert galaxies show an enhanced small-scale density segregation with respect to LINERs. This gives support to the idea that AGNs can be stimulated by interactions. On larger scales, tens of Mpc, we find that the AGNs hosted in luminous early-type spirals show a tendency to stay near the center of the Local Supercluster. Finally we discuss the interpretations of our findings and their consequences for some possible scenarios of AGN formation and evolution and for the problem of how AGNs trace the large-scale structures.