Try a Segway tour, or how about a day at an archaeological dig? You could plant a tree in the Jerusalem forest, take a hike or spend an hour or two in the open-air gym at Sacher Park.
Walking through the Old City--whether it's traversing the ancient alleyways and markets, following the Via Dolorosa, or climbing up the walls and encircling the city from the ramparts, will give you a new appreciation for the history that's contained in those walls.
If all that's not enough to burn off your energy--head over to the City of David where, after descending hundreds of stairs as you walk through layers of history all the way back to Canaanite times, you'll be able to wade through a 3,000 year water tunnel.
On the way back, you can either hike back up the steps or take the easy way out by waiting for the shuttle van to transport you to the entrance that's not far from Dung Gate.
1 Keren Kayemeth LeYisrael
P.O.Box 45210
Old City
Dung Gate
Shiloach village
Various places in the city
(St Stephen Gate to the Holy Sepulchre)