We just got back from Disney, and the kids spent an evening at the Neverland Club. DS is 6 and has sensory issues, DD is 4. They really enjoyed it. The only complaints that DS had was that it was loud, that there alot of kids and that it was dark. He was able to deal with that, but I'd be careful if your kiddo has problems with any of those things. There were alot of activities to do including arts and crafts, dress up, video games, movies etc. From talking to my son and observing them there, it doesn't seem like any one child gets constant supervision, its more like there are people in each room who deal with potential problems so that thrilled both of mine that no adult was shadowing them. We were told that they do not deal with bathroom issues, that the child has to go in and manage everything on thier own. We did not leave the resort (well, we did after 2 hours, just to have something to do) just in case there was a problem.
If you are looking for a night out, without alot of worries, Id go with the in room babysitter. I've heard good things about them and your DD would be in a familiar place with one person focused on her- so they could do what she wants, not what alot of other kids want. I know for us, I was NOT relaxed with the kiddos at the Neverland Club, I wasn't worried, but I was on edge waiting for a page from them.
HTH
Bri