Mount Nebo is a ridge that rises 817m above sea level about 35km southwest of Amman. In the Old Testament, Mount Nebo is where Moses first glimpsed the Holy land (and where he was later buried). The view has not changed. It's simply breathtaking. On a clear day you can see all the way to Jerusalem. Be sure to go in the afternoon or evening on a clear day, because the view isn't as good in the morning.
Aside from the view, there are archaeological remains from a fourth century church. There are several magnificent mosaics. There are also remains of a Byzantine Palace. The pope visited here in 2000 and planted an olive tree, which is still there.
To get to Mount Nebo, you're first going to want to catch a bus to Madaba. From their, taxis and minibuses make the short trip to the mountain. If you want to get there directly from Amman, you can take a taxi or go with a tour.