One of my kids' favorites, and a really on-point bedtime song, is BNL's "When You Dream". This video ain't exactly quality, but it was about the best I could do for a live performance. The album version of this song is definitely worth a listen, and the lyrics are pretty fun too.
Obviously not a song I sing to my kids, but one I'll often play as they're drifting off to sleep. It has become one of my favorite pieces, and I think this performance nails it (minus the coughing audience members). Right about 2 minutes in, when it almost seems like the song could be winding up, but then it shifts into an other-world quality... perfectly dream-like. I haven't stopped being wowed by that, despite hearing the song probably a hundred times.