Assuming no other changes to radio technology, then the best way to move radio waves between caverns would be to use wave guides. Waveguides are simply metal pipes or ducts that confine the waves within and allow them to propagate over long distances without attenuation (the spherical waves emitted from a typical dipole antenna fall off due to the inverse square law, besides being absorbed by the cavern materials).
In practical terms, a transmitter would have one or more wave guides fanning out towards the various connecting passageways to the other caverns it is meant to service. the ends of the waveguides can be left open at the entryway to the other cavern, to allow the waves to propagate into the cavern and let people pick up signals. This would be fairly efficient for one way broadcast radio (much like real radio even today), but you would not realistically be able to transmit two way traffic like WiFi or VHF voice radio in this manner, unless the transmitters and receivers are placed at each end of the waveguide. At that point you may as well use wire as the transmission medium rather than radio waves. The other issue is the waveguide will have to extend into each cavern you want to transmit to, so if you have a string of caverns, then the Cave Broadcasting Corporation "World News Service" would need a maze of waveguides leading into each cave. This would be rather inefficient, and eventually there would be signal loss at the end of the longer waveguides. Depending on the frequency being used, the radio waveguides might also be rather large, which could be a problem if the passageways are small or have very sharp corners, and also if multiple radio stations are trying to broadcast (imagine a service corridor with lots of pipes and ducts to get the idea).