A unique Irish pub that I like is Waxy O'Connor's on Rupert Street. It is between Piccadilly Circus and Leicester Square.
There are two entrances one on Rupert Street and the other on Wardour Street.
Must of the pub is in the basement and looks like something out of Harry Potter. There are loads of balconeys, staircase etc with a tree right in the middle of the pub.
I guess it will be quite busy on St Patricks day though!!