Don’t skip the obvious and typical- which for a first timer are especially meaningful- like walking tours of the Old City and visiting its many attractions (such as the Kosel tunnels, southern wall excavations, burnt house, rebuilt churva shul, etc etc.). Exploring the various neighborhoods around Yerushalayim, like Geula, Meah Shearim, Machane Yehuda shuk, Yemin Moshe.
MiniIsrael (near Latrun) is nice, and you get to see all of Israel at once (in miniature).
The Israel Museum has some interesting stuff and model of the Beis Hamikdash.
Tzefas, Old City, the old beis kevaros
Pretty sites in the Galil- like Rosh Hanikra, the Banyas and lots of nice hikes.
Yam Hamelech and Ein Gedi.
Tour a winery (there are many, large and small, such as Carmel Zichron Yaakov).
skiing in the Hermon (if you are coming soon before snow melts)