Nothing was too much trouble for the staff at the Mount of Olives Hotel.
There is no AC but the wind howls around the building at night (in a pleasant way) which makes it cool. The neighbourhood is certainly noisy day and night and, yes, the call to prayer from the mosque can be loud, but I enjoyed the experience, personally.
I caught the bus back to the hotel every evening but i did so no later than 7pm, and then took an early night. If you are staying out late, I would probably recommend using a taxi to get back. Certainly do not walk on the Mount of Olives (the actual mountainside where all the churches are) at night as this is a well-known thieving hotspot.
The breakfast is good, Internet access is excellent, the staff can arrange taxis and tours quickly.
The Mount of Olives is a Palestinian area. This caused me no problems but it is worth noting as it is true that some taxi drivers in Jerusalem will refuse to take you there, and only Arab buses (departing from the bus terminal at Damascus Gate) go there.
My room was basic, but good. There was a safe in the closet.
They serve dinner, but also recommended to me a restaurant around the corner. I forget the name but it is the only one of the 2 nearby restaurants the hotel staff will recommend. It was wonderful: great food, great decor, friendly people.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC