The Cave of the grotto was okay. It was disappointing because they now charge. There isn't much to see except the chapel in the cave. If it is really the cave John wrote Revelation in than it worth visiting. There is nothing else to see there though. You don't get to see any of the monastery. If the cave doesn't interest you, it isn't worth the money. The web site says modest dress required so I followed directions but there were people there wearing bathing suits with little cover ups which surprised me (they probably don't care since they charge now).
If you aren't already in Patmos it isn't worth making the effort to go to Patmos just to see this.