I was using Stellarium to watch Saturn from its moon Pan and I saw the rings were very close to this moon. Now Saturn's rings extend for a large distance so several moons see them from close. I was wondering, is it know which Saturn moon passes closest to Saturn's rings and at what distance?
Pan, Daphnis, and various other moonlets, I would argue, are inside the rings.
If you explicitly discount the Encke gap (which Pan orbits in) and the Keeler gap (which Daphnis orbits in) as being part of the ring system, Daphnis would be your answer, as it is a ~8 km object in a 42 km gap. (for comparison, Pan is a ~35 km object in a 325 km gap)
Really, your answer depends on what you want to consider a moon. There are many objects small enough to be classed as moonlets (several hundred metres across) embedded in the rings, and presumably countless more of smaller size.