We returned from Celebrity Infinity a couple of weeks ago. The kids' facilities were pretty extensive. There was a ball pit, large TV for seeing movies, computer stations, to name a few. There is also a pool just aft which also has colorful slides and other equipment. Once I download my photos (I'm way behind), I'll post a few links on this thread. There's also a virtual tour on the Celebrity Web site (go to Millennium, Virtual Tours, Sunrise Deck) for a quick view of the space.
I didn't save any of the activity sheets, yet some of the kids' events I recall were pizza parties, scavenger hunts, talent show, and a visit to the bridge. The last one is pretty cool as only the kids were allowed -- no adults.
I can't give any reviews as our son didn't participate in the program, but he did go in with us once toward the end of the cruise and enjoyed it. (He's the type of kid who likes to spend time with Mom and Dad.)