Photo: Joneikifi, CC BY-SA 3.0 via Wikimedia Commons
This is the highest peak in the area. At the top you will find a small church and the tomb of Aaron, brother of Moses. The route to the top and back will take you past the Monastery and will take 4-8 hours depending on your chosen path.
© OpenStreetMap contributors
If you follow the track further from the Monastery, you will reach a camp offering tea and stuff to sell, which offers a great view of the desert to the west.
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The largest carved monument in Petra, dates back to the 1st century AD. The interior, like that of the Treasury, is underwhelming in comparison to the façade. The more than 800 steps up to the Monastery can take over an hour, and even if you take a donkey you will have to walk and climb for about 10 minutes near the end.
The site at the top of the mountain contains elaborate rock altars used for sacrifices. From the High Place, one can view much of Petra from above. Beautiful scenery. It can get cold and windy up there. The trek down the back side of the mountain reveals many interesting tombs and carvings that might be missed by the average tourist. The round trip generally takes 1.5-2.5 hr. Not many people go through the back route as it's not always clear where it starts - ask or use OpenStreetMap to identify the track. You might even try to use the direct track to the Treasury, which is even harder to find and not official, even though the staircases are clearly visible from down the Treasury.
At the end of the Street of Facades is the 7000-seat Roman Theater. The theater was created by the Nabateans but later enlarged by the Romans. It is still used for occasional performances.