The Cavern is the most famous club in the world.  It’s also one of my favourites.
Designed/rebuilt to look carved out of rock, the aptly named Cavern has a small stage at the front of the underground main area which once, obviously, launched the Beatles to fame.  There is a back room with a larger performance area as well for bigger gigs and private parties.  There is an atmosphere throughout though, because of its history, which means that any gig at the Cavern feels special and this is possibly why some bands still have ‘secret gigs’ there to try out new material in an intimate venue where so many iconic bands have done the same previously.
The Cavern is on Mathew Street, the whole of which is more-or-less a shrine to Liverpool’s most famous sons, with the majority of the bars given a Beatles-themed name and a bronze statue of Lennon upon it.

tip: After seeing the Cavern and Mathew Street, do this....
Find out where it is (because it’s moved to new sites regularly, but it’s currently on Tithebarn St near the gardens) and go and laugh yourself sick at the SUPER LAMB BANANA.  If you don’t know, in brief, a Japanese artist sculpted it out of concrete and fibreglass and said it was designed to represent Liverpool’s historic exports (sheep & bananas?) combined with a dire warning about genetic engineering (???).  It is an 8 tonne, 17ft high sheep, spliced with a banana and though it has been painted various colours since its creation (usually for charity purposes) it is generally bright yellow.  It is one of the funniest and most pointless things I’ve ever seen, but I have really come to love it and so have most of the people of Liverpool.