I visited CERN last July. Was lucky enough to get into a group tour. The tour guide was a postdoc researcher who said the only times that public tours are allowed to take an elevator down is during long shutdowns. So while they do this work on LHC might be the best time to swing by for a tour (I might even try to return).

Even without the descent, my tour was great with showing the 70 year timeline, historical early particle accelerator equipment, and a cool view of the ATLAS control room. The facility is awe inspiring and a testament to Europe's willingness to make long-term commitments to furthering science research for the public good.