I've done both trips - wore my regular walking shoes with socks to the ruins and "fake tevas" on the cave tubing jaunt. I didn't do so well with the tevas - I was slipping and didn't have my footing as well as I needed to - but then, at that time, I was 100lbs over weight (which is not the case today). Just another perspective.
Have fun - those were two of my favorite experiences!