We stayed in the Hotel Kaplan for two nights for exploring Jerusalem and this hotel is perfect. The location is about 15 minutes walking from the New gate entrance to the Old City and a bit more to the Jaffa gate.
I would definetely prefer this hotel over accomodation in the Old City since it is just minutes away from the nightlife of Jerusalem. That makes the hotel a bit noisy, but if you are into some pub crawling after your sightseein, this is perfect.
The rooms are nothing fancy, but clean and okay for the price.
The owner can be reached via Tel: +97226254591 or natan_taig@yahoo.com.

We stayed for 5 nights and were very pleased. Our host Eli was welcoming and very helpful. He let us use his kitchen and refrigerator. Kitchen was small but very cosy. Eli always kept fresh veggies there for everyone. He taught me how to make good turkish coffee and even went to the supermarket and bought me good brand to take home. We had a triple room with a balcony. Beds were relatively small but comfortable, especially after walking for 10 hours every day. The only thing that took some getting used to and could potentially surprise our fellow Americans was tiny bathroom with shower but no basin, so water was all over the floor. Apparently this is not uncommon in Europe.
The main advantage of this hotel is location. it stands on the quiet side street off Yaffo road near the intersection with Ben Yehuda (area filled with restaurants, cafes, etc.,) On the other hand it is only 7 min walk from the the entrance to the old city via Jaffa Gates

p.s. the hotel photo of this hotel seen on the internet is NOT the Kaplan Hotel. The "lobby," hallway, kitchen area (if you want to use it), rooms all reek of recent, current and stale tobacco use. Guests are allowed to smoke in their rooms. It stinks everywhere. If you stay on one side of the hallway expect a really loud party from the young neighbors in the facing building if your timing is unlucky. If your timing is fine and the neighbors aren't having a party til 2 a.m, you CAN expect to hear pigeons just above your room flapping loudly from around 5 a.m., and soon they'll begin making pigeon moaning sounds til sunrise. If you stay on the other side of the hallway (the same side as the office) you will have to endure the loud music from the ice cream joint across the street every night til midnight (except on Friday night, as that's shabbot). BRING YOUR OWN GAS MASK if you have kids, are middle aged or older, don't like secondary and stale smoke everywhere and if you have even a hint of asthma.

We spent hours looking for the perfect budget hotel/hostel in the perfect location for a family trip including parents and siblings and spouses. The Kaplan is smack bang nr Zion sq, great for shopping, for eating out for drinking and for a short walk to the Old City. We booked 3 rooms in advance and the wonderful owners kept in contact with us, made sure our late arrival wasn't a problem and made us feel very welcome for our stay. Tea / coffee/ fee Internet......exactly what we wanted. They helped us research into the next part of our trip too. Best of the bunch!