Among some of the places:
Visit Al Aqsa mosque, West Wall, stroll in the old city streets, if you like you can go to the Islamic museum that contains one of the largest clock exhibitions in the world, Machneh Yehuda open market, Mamila quarter with it's mall is very nice
You can consider taking one day tour to the dead sea and surrounding.
You can ask the hotel to give you maps and more guide.
I hope that will help over 6 years ago