If you try to plan your route throughout Palestine, you’re kind of left alone. Popular map software shows streets but no street names and only some limited points of interest. Open Street Map helps you out; but the ignorance is a political signal. Some areas and routes are defined as no-go places. By good reason?
Currently the situation in Israel is mostly uncomplicated. You might visit Bethlehem, Ramallah and Jericho (but better keep away from Nablus or Hebron). Car rental companies divide the Westbank into two parts: Those controlled by the IDF and those controlled by Palestinian forces – and the latter you are not allowed to go to by rental car (not covered by insurance).
If you want to see Bethlehem or Ramallah, go by taxi. You can catch a Palestinian taxi at the Damascus gate at Jerusalem. Going to Bethlehem felt safe. Gaza for sure is out of reach. In contrast to the Westbank, the Gaza strip is in the hand of Hamas and Israel has locked all border crossing points since 2008 (not without a cause, but creating a very problematic humanitarian situation).