Israel

I'm likely to get flak for this response, but here goes anyway. The Old City is not a good place to stay: 1. There is no public transportation and some hotels are not accessible even by taxi, so you may have to carry your luggage over cobblestones and perhaps stairs. 2. Pretty much everything closes around 7 p.m. So you will have to go outside the Old City for dinners, shopping, and sight-seeing. 3. It's kind of spooky, though not necessarily unsafe, to walk through the streets when it's dark and deserted.
4. There are many more places to visit outside the Old City than inside it. So while it may be convenient to be there to sight-see in the Old City, it will be much less convenient to visit other places. Unlike the Old Town sections of other cities, Jerusalem's is completed surrounded by stone walls and most of the streets were built before the horse-and-buggy days. The streets had to be only wide enough for a fully-laden donkey to pass through. And so they remain to this day. Modern Jerusalem grew up around the Old City and there are many hotels within a few minutes' walk of one of the Old City gates. The heart of the modern city is a 10-15 minute walk. The Harmony Hotel is very popular with tourists. The Notre Dame Guest House is across the street from the New Gate and a 5-10 minute walk to the center too. A bit farther away is St Andrews Scottish Guest House, not quite as central, but a good deal cheaper. There are lots of other options. I suggest you use Trip Advisor to search for hotels. If you have more questions about location, send me a private message and I'll be happy to help. You haven't given your dates. May 14-15 is the Jewish holiday of Shavuot and May 8th is a holiday in Jerusalem. Rates are likely to be much higher around those dates than the rest of the month.

We stayed at the Austrian Hospice and loved it...especially the view of the Old City and the Dome of the Rock from the rooftop! It's right on the Via Dolorosa. Check out their reviews on Trip Advisor.