Comment by DoubleFree

Space is not quantized, so yes, the electron has infinite possible locations. There are, however, places the electron cannot be, depending on its energy. See, the electron's energy is quantized, meaning it can only have a predetermined set of values (see atoms' electron shells). The energy determines the wave function and the wave function squared is the probability distribution for the electron's location. This wave function has roots, indicating where the electron cannot be.