Are you really sure that you wouldn't rather re-read the second book. I think that this would be much better than having it regurgitated back to you in third person.
I will tell you this, in New Moon, Edward does something that he promised never to do and no reader could ever have seen it coming. After this incident, Bella has to deal with some very strong emotions and even more difficult decisions. Jacob plays a much larger role in this book and it is his friendship that helps her through this tough time.
While Bella deals with her own issues, Jacob has his own "drama" to sort out. He too has some decisions to make. He's carrying a very big secret that he fears may injure his friendship with Bella.
If you enjoyed reading Twilight, you are going to LOVE New Moon.