Babbo is superb. It does help to be a little flexible when it comes to proteins (no chicken breast on the menu) but the flavors are phenomenal as is the wine list. There are plenty of threads about what to order. Try the links below and do a search of your own and you'll have plenty of help. Enjoy.
I didn't think it was very good, unless you are a fan of entrails...which seems the majority of the menu. Loud music- and I'm a fan, but if you can't hear the server....hello??? Celebrity chef hype, if you ask me. There are so-o-o-o-o many good restaurants in the city, there's no need to go here, in my opinion.
If you want a great place where the chefs hang out, try Blue Ribbon. I had one of the best meals of my life there, and it was totally unexpected, unpretentious and great service. (1st shrimp dish on the menu.)
Good luck and Bon Apetit!