Special permit are required to hike to The Wave (just ten are issued for each day). Permits ($5 per person) can be obtained in advance (http://www.blm.gov/az/st/en/arolrsmain/paria/coyote_buttes/permits.html)
Beautiful cave, some stalactytes are impressively massive. You can explore just first 1km where the path is built or if you pay much more you can go deeper into the darkness with a guide. That would be a great thing to do there!