St. Peter in Gallicantu
You can't quite make out the golden cock above the black cross in this picture, but you might notice the church is modern, dedicated in 1997 on the site of an archaeological dig which was examining the ruins of older Crusader and Byzantine churches on the site of what is believe to be Caiaphas's house, where Jesus was taken after his arrest and tried. Artifacts from the excavation, including several 5th-century Byzantine mosaics, are displayed around the church and its grounds, which also include carvings that represent the story of Jesus's arrest and trial.
As with most Jerusalem holy sites, much of its significance is conjectural. For example, the archaeological team discovered a cave complex beneath the foundations of the oldest building, which some argue is the place were Jesus was imprisoned, though there is also a candidate for that in the Church of the Holy Sepulchre. They also don't even bother to post a sign for a possible spot where Peter denied Jesus three times before the cock crowed, the incident which lends the site its name. Regardless of the particular events, though, you have to feel respect for the place just because of all the pain it bears from those who come here on pilgrimage seeking to understand the Passion.
It's also great for the views overlooking the Kidron Valley. I walked back downtown along the edge of that valley, as well as the Valley of Jehoshaphat, which is simply its central portion and located between Temple Mount and the Mount of Olives. You can see some pictures I took here.