I travel about three to four times a week by car for work back and forth to the Old City of Jerusalem from Ramallah. While it is only about 11 miles, it feels much farther because it takes about one and a half to two hours due to military checkpoints and traffic. Also, traveling to Jihar Valley for hiking took about one and a half hours to head southwest of Ramallah toward the Valley.
A lot! The Palestinian Territories and Israel are about the size of the state of New Jersey for reference. Since the start of my journey, I've traveled to major cities in both places such as Tel Aviv, Bethlehem, Jericho, Jerusalem, Ramallah and Jenin; some cities more frequently than others. Also, since the start of my journey back in September, I've traveled to the U.S. (Florida and Washington D.C.), Jordan, Bosnia and Herzegovina.
I drive myself. I have a car with a yellow Israeli license plate which allows me to drive within both Israel and the Palestinian Territories.