Loosely speaking, East Jerusalem refers to the Arab neighborhoods controlled by Jordan in the years when the city was divided (1948–1967). That includes the Mount of Olives, and the areas north and southeast of the Old City.
The sights in this area are for the most part distinctly Christian. A few are a little off the beaten path, and the best way to explore them—if you're energetic enough—is on foot. If you're driving, however, you can sometimes find free parking at the Seven Arches Hotel on the Mount of Olives and paid parking at the cluster of large hotels near the American Colony; or take a cab.