New Year's Eve is a blast! The Champs d'Elysses is amazing with all of the people. You need reservations at most of the restaurants and many will be closed down, but just walk around when you first get to the city, see one that you like and ask if they have room that evening. I've only had to wait once when I've done this and during the entire wait I was provided with free kirs, champagne, and wine!
As far as the museums, I believe you can purchase the ticket at the metro which will save a great deal of time. If you are planning on visiting many of the sites, it really is a time saver. You can also purchase them inside the Louvre, but the line for it is incredible (of course, if you're only going to be in Paris for a couple of days my recommendation would be to skip the Louvre and go to the Musee d'Orsay and the Musee Montmartten instead, but this is just my preference).
Some of my favorite restaurants:
L'aubergine (near Invalides - L'ecole Militaire) The owner is American/French - worked in Florida and New York for many years before opening this place. He is sooo gracious.
La Table Ronde (Sentier district) - incredible duck!
Many of the restaurants may be shut for the holiday, so check before going (even if your hotel says it's open, I'd still go and check to avoid disappointment).
You really can't have a bad time in Paris.