I imagine your tour is going to include the major sites in and around Jerusalem: the wailing wall, the dome of the rock, the tomb of Christ, etc. If not, you should really check them all out, no matter what your religious persuasion is. Even if only as historical sites, they're fascinating, and some of them involve beautiful art and architecture.
The whole of Yad Vashem is quite compelling, one of the better museums I've been to, though given the subject matter, it can obviously be heartbreaking.
If you like gardens, the Baha'i center if Haifa has one of the most famous botanical gardens in the world.
Masada is, if nothing else, a fascinating historical site.
I also remember the hike up Mount Sodom being really cool if you enjoy hiking.
If you can afford it, get tour guides when you can. Guides in Israel are highly trained and licensed, and they really know their stuff.
Probably the best thing I did in Israel was not something tourists usually get to do: the group I was with was invited to have dinner at the home of a Bedouin chief and his mother. Some of the best food I've ever had. So I guess I'm saying, if you have a chance to make friends with someone interesting, do it.
I arrived just after Christmas, but I was there for New Years. I seem to recall it being not as big a deal there because Jews and Muslims each have there own New Years. I was in Jerusalem, though. More secular cities like Haifa or Tel Aviv might make a bigger thing out of it. I remember there were some younger people partying on this one street on New Years Eve, but other then that I seem to recall it being business as usual.
A word of advice: the security at the airport there is incredibly tight. Sometimes you move right through, but if something about you strikes them as even a little suspicious, it could take a long time to get through all of the bag searches and interviews they put you through. So go early on the day you leave, like much earlier then you would in the States or in Europe. If you have to spend a few hours reading a novel, it will probably be worth it.