I stayed at the MGM very recently (about two weeks ago). There were three of us under 21 (though over 13) and two adults. I don’t know about the others, but here’s what I liked about it:
* They have live lions during the day, though all they do is sleep (it’s their natural behaviour, but may be not so interesting for the baby)
* M&Ms World is just outside. Not a place to leave the baby, (it’s a four-storey M&Ms-themed merchandise store) but freaking awesome anyway, not sure if you have been to one before. (The Coco-cola shop is next to M&Ms World, but is not as good.)
* The monorail is accessible from inside the hotel, so you don’t have to spend as much time on the street if you want to explore the strip.
* Very clean, big rooms, not sure about arrangements for baby cots work. We chose not to drink the tap water there, but then again we didn’t drink the tap water in any hotel in the USA.