Check out the Kaver of Shem and Ever in Tsfas.
Take a dunk in the mikvah of Avraham Aveenu in Hebron and Daven neitz by maaras hamachpela.
Check out the Shul/Mosque by the Kever of Shmuel Hanavi outside of Ramot in Jerusalem.
Take a hike through Lifta behind the central bus station in Jerusalem and take a swim in the natural mikvah.
For sure daven kabbalas shabbis by the kotel, go to a few tisches that night like Belz, Dushinsky.
For a beautiful view, I might check out Mitzpe Ramon, although there is not much else there and it is a long drive.