Geez...No not like in Res.181. The UN Should have no authority of its own Bathrooms let alone Jerusalem. But It should be there, instead of in Manhattan.
Remember, Arab diplomats make up a substantial proportion of that body. Then you get to step B, Building 2 embassies for every member nation, near and around Holy sites.
It makes those that support the current Palestine regime, have a very personal stake in the security and peace of the area. (Not to mention that that kind of project develops a commerce structure of its own, bringing Capital, and improved standards of living to the area....etc...)
(Sort of like merging a modern version of DC, with the Holy sites as hallowed ground.....)
I'd say move it to Cairoor Riyadh, but the diplomats wouldn't like the nightlife. Let the Swiss have them.