There are vaults beneath South Bridge, George IV Bridge and Waterloo Place, with only about 10% of the South Bridge Vaults open to the public. There are five streets beneath the City Chambers. Three of them are Mary King's Close, Stuart's Close and Pierson's Close. Not sure about the other two. Besides that, theres not much else besides millitary bunkers. There is a myth about a tunnel that links the castle and holyrood palace but noones ever found it.