If Jerusalem was a international zone controlled by the UN it would keep the peace between Isarel and Arab Nations, while making it further possible to have a Two State solution between Israel and Palestine. While it'd be hard to do it would be the best solution we would have to ensure peace for years.
While, in principle, it may seem like a good idea to put Jerusalem under third party administration, that alone would not magically bring about peace, nor would it even begin to address the grievances on both sides. The Palestinians openly state that they want the WHOLE state of Israel, not just one part. They want to drive the Israelis into the sea. Israel, while increasingly more tolerant of a 2 state solution, will never agree to give up Jerusalem. A third party will only become another target for extremists, just as the British were when they were in control of Israel/Palestine. Just as the US cannot be reasonably expected to keep armies in the middle east to protect the peace, so too will a UN protectorate become untenable. The problems in the regions must be solved by the parties themselves if true peace is ever to come. That means Israel and Palestinians must work together.