We have been twice, pre dd.
My hotel reccomendation would be the Venetian, every room is a suite and it has a gorgeous interior.
As for taking the baby, I'm not sure. We did the casinos, shows on a night, and loads of sightseeing, none of which were really suitable for kids. Didn't really notice things for children to do, as we went before we had them.
We didn't do the helicopter, but my parents have and said it was expensive but breathtaking. You can go on a small plane type thing (excuse lack of technical terminology) which seats about 16 and is cheaper, I believe.
We also hired a car and went to LA for the weekend, we drove through the desert and it was the highlight of the holiday. As I said though, not really suitable for a small child, and very very hot(we went in April/May)
Definetly the best holiday we have ever been on. I do kow someone who has taken dcs but they were much older and could enjoy the shows and sightseeing. And you are right, no children in the casinos, and bear in mind these take up the entire ground floor of most hotels, and are a welcome escape from the heat.