Here is my experience.
Background: DS was 2 at the time, goes to full time daycare (he had just switched to a "center" before that he had been in an in-home). I also have a DD who was 4 (she went to the kids club).
First to answer the question, I believe the have swings.
The nursery was split into 3 parts. Part 1 is where you drop child off, there is a desk & then a door, split into 2 halves that you drop the kids off. They get passed through the top half. Part 2 is the "play area". There were toys, ride on toys, a ball pit (if i remember correctly), a play mat, etc and a TV. Someone in a review thought this was a small smace, it seemed about right to me, however. Ample room for the kids without too much room that you might lose one

. Part 3 was the snack/quiet room. They had cribs & small tables. I think the swings might have been back here, again, don't quote me on that one.
My son at the time had extreme seperation anxiety when I would leave him, he did this at daycare so it didn't surprise/stress me. I am the type of mom (judge away) that can leave my kid crying & not be upset by it. I know that in less than 5 min he will calm down & all will be fine with the world. And that is exactly what happened. He had a ball. We would leave him here & there sporadically & then from about 7pm until bedtime (8-8:30 depending on the night) so we could enjoy dinner. I did not inquire as to what he did each time, just picked him up. Then, on the last night we got to our cabin to find a delivery from the nursery. They had made scrapbook pages of him having a grand old time. I loved it! They were precious & I knew that he was full of balony & enjoyed himself.
I did take him to the open house the first day, but it didn't really help break him into the experience. He was too mommy clingy at the time.
I would leave him again in a heartbeat, probably for more time in the future, but he'll be in the kids club on our next cruise.