Glycolysis occurs in the cytoplasm (specifically the cytosol) of the cell.
Location in the cell
In both prokaryotic and eukaryotic cells, all the enzymes for glycolysis are dissolved in the cytosol, so the entire pathway runs there rather than inside an organelle. This contrasts with later stages of cellular respiration, such as the citric acid cycle and oxidative phosphorylation, which occur in the mitochondria of eukaryotic cells.