Barkai studio is the perfect place to stay in Jerusalem: the location is excellent, just 5min from Damascus gate and New gate. So you can basically walk everywhere in the Old City, go to Olives Mount easily, and Jaffa Street and the new city are also about 10min walk.
We had the garden studio which is very nice, you can eat outside. It is quite big, has a nice bathroom with shower (and a blowdryer) and small kitchen. There is free wireless internet if you happen to bring your laptop with you.
Most importantly, the owner Ruti is very helpful with all little things like booking sherut, checking transportations etc... and it makes a real difference.
I really recommend this place and would stay there again.