When I saw "n" in the title I assumed they wanted something that worked reasonably for large n. Rejection is no good because of the notorious "curse of dimensionality". So my idea was to choose a suitable distribution on the radius, then draw from it and choose the angles at random (not sure what those angles are called). You might have to delete the point at the center for that to work.

Maybe n=4 if you have a timestamp as another dimension.

Most of my code has bad asymptomatic bugs but they never show up in testing because the tests don’t have data sets big enough to show the symptoms!