If you are looking for large spaces to run around and let off steam in Jerusalem then there are some good options available. One of my favourites is the stretch behind the King David Hotel (running from the French Consulate past the Monetfiore Windmill down to the Begin Centre.) It has a shady area under some tall trees and some of the most spectacular viewpoints over the Old City.
It is a great place for the adults to relax and take in the views and the children to run around; although in absolute terms the only ready made activity is hide and seek; but bring along a ball, frisbee, cricket set and you are set up for an hour or two of downtime. This area is readily accessible from the main hotels, or at the end of an Old City touring day.If you want to stretch your legs then you can explore the nearby gardens, Yemin Moshe & Mishkenanot Shananim.
Just across the road is Liberty Bell park (down the hill from the King David stretch) which is also popular – a real playground, outdoor cooking, sports and a fun place to be.
Another good option is Independence Park at the back of the Sheraton Plaza Hotel with access from Agron Street and stretching towards the centre of town. Large spaces to run around; a good coffee shop for refuelling on the way. Independence Park is a natural short cut near down town offering a few minutes to relax after an intensive shop and eat session.
If you are out by the Israel and Bible Land Museums then a good option is Emek HaMatzleva & Gan Sacher – a pleasant walk (near the olive trees and Monestry of the Cross) and then one of Jerusalem’s largest parks.
All of these sites are wheelchair accessible.
See Jerusalem Playgrounds for more ideas.