Looking at the radial probability of observing a 1s electron at a certain radial distance we see one peak (can’t put pictures in this forum). First of all, the probability density is completely spherically symmetric, meaning the probability does not depend on the azimuthal and elevation angle, only on the radial distance r. So the electron can be anywhere, very close to the nucleus or very far, but on average it will spend more time near the peak because this is where the probability is highest.