Context: For the first time, spectroscopic galaxy redshift surveys are enabling galaxies to be studied with the nearest quasars. This allows the dependence of the activity of a quasar on its environment to be studied in a more extensive way than before. Aims: We study the spatial distribution of galaxies and properties of groups of galaxies in the environments of low redshift quasars in the Sloan Digital Sky Survey (SDSS). Our aim is to understand how the nearby quasars are embedded in the local and global density field of galaxies and how the environment affects quasar activity. Methods: We analyze the environments of nearby quasars using number counts of galaxies. We also study the dependence of group properties on their distance to the nearest quasar. The large-scale environments are studied by analyzing the locations of quasars in the luminosity density field. Results: Our study of the number counts of galaxies in quasar environments shows an underdensity of bright galaxies at a few Mpc from quasars. Groups of galaxies with a quasar closer than 2 Mpc are also poorer and less luminous than average. Our analysis of the luminosity density field shows that quasars clearly avoid rich superclusters. Nearby quasars seem to be located in the outskirts of superclusters or in the filaments connecting them. Conclusions: Our results suggest that quasar evolution may be affected by density variations both on supercluster scales and in the local environment.