If you want to visit Atlas (control room) or CERN’s first accelerator (a synchrocyclotron) just show up in the morning when the visitor center opens. The tour guides are often passionate scientists. The museum is worth visiting, you’ll get to see the first www server (Tim-Berner Lee’s nextcube). The live shows are well put together. And everything is pretty much free of charge.

The only thing I can think of that has a waiting period is if you want to visit the actual tunnels, you can only visit them in between experiments (every 10-20 years maybe even less often).