Rabbi Eliyashiv,ZT"L,ZY"A was a big gadol & posek,however being born in Lithuania he was a pachdan when it comes to Goyim.
Did he site any rational halachic reason? No.
I personally don't go because I am unsure which parts are mutar,however those that do go should go under halachic guidance a rov who knows.
I believe if Rabbi Moshe Feinstein,ZT"L,ZY"A did not rebuke his son in law Rabbi Moshe Tendler for going up I assume it is okay as if there was a problem Rav Moshe would have rebuked his son in law.
Rabbi Tendler does know the areas that are permitted.