For Dunn's, wear any type of shoe that you can wear in the water, won't slip off your feet, and have good traction for walking on rocks. I wore a pair of Nike water sandals, others have worn those water socks.
For the Island, throw a pair of flip flops in your bag in case you want them while you're walking to and from the Tower or the bar, but they aren't required.
We are also going to CTI in Feb. We picked up some cheap water shoes from Walmart for the Dunns river falls. They were about 6.00 a pair. I was surprised to see that Walmart had them at this time of year. It is -44C here today! BRRRR!!!!
I have a nice set of sebago water and deck shoes. They worked good for comfort and stability while climbing, however, the sealed up normal shoe nature of them would cause sand to get in there. I stopped and emptied them a couple times but shortly after they had sand in them again.
I like the closed toe protection of those types of water shoes, but an open heal type water sandal/shoe thing might be better in that sand would flow through without issues. I think Keen makes some nice ones. They are like fully covered active sandal type footwear but offer a bit more toe protection and a sole.
Those keens are $75-100+ so unless you're going to wear them at home, stick with something cheaper. You can also rent water shoes on the way there for $5 but they smelled pretty nasty.
We couldn't find any in stores here so I found some online at West Marine for $15 and my wife found some clearanced at Lands End for $7.50. Hers were more like shoes and mine were sockish. Both worked really well for the falls.
Water shoes or old sneaks. Sneakers take forever to dry though. Flip flops are not recommended for the climb as they will fall off your feet. For the island, flip flops are nice to wear especially in the bathroom. Also the concrete and decking get hot so it's nice to have them to walk to and from the bar. You don't HAVE TO HAVE anything, though.