You will have towels in your stateroom & near all of the pools on deck. In addition, they will pass out towels as you leave the ship (or even at your meeting place) for your excursions and your day at Castaway Cay. No need to bring your own unless you like the larger beach towel style. The towels onboard are typical hotel towels.
You can take all the towels you need from the cabinet. Unlike RC and Carnival who make you sign them out then charge $20 per towel if it's not returned to the towel desk.
The only towels they definitely hand out is at CC. There were no towels handed out at the gangway while in Cozumel. They did have some towels on a table set up on Grand Cayman but not near the gangway but in the plaza when got onto Grand Cayman. In our cruises we found the only place they hand the towels out consistently is at CC. The other ports on the Eastern itinerary are hit or miss.
If you are on a DCL excursion they will hand towels out at your excursion meeting place onboard.
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