Question: Two ships of the Royal Navy have been named HMS "Leonidas" after Leonidas I, king of which ancient location ?

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HMS Royal Charles: Two ships of the British Royal Navy have been named HMS "Royal Charles", both after King Charles II.

HMS Mansfield: Two ships of the British Royal Navy have been named HMS "Mansfield" after Captain Charles Mansfield who commanded HMS "Minotaur" at the Battle of Trafalgar:

HMS Gurkha: Three ships of the Royal Navy have been named HMS "Gurkha, while two have been named HMS "Ghurka, after a people who originate in Nepal and who serve with distinction in the British Army as part of the Brigade of Gurkhas.

HMS James Watt: HMS "James Watt" was a 91-gun steam and sail-powered second rate ship of the line.  She had originally been ordered as one of a two ship class, with her sister HMS "Cressy" , under the name HMS "Audacious".  She was renamed on 18 November 1847 in honour of James Watt, the inventor of the steam engine.  She was the only Royal Navy ship to bear this name.  Both ships were reordered as screw propelled ships, "James Watt" in 1849, and "Cressy" in 1852.  "James Watt" became one of the four-ship "Agamemnon"-class of ships of the line.  They were initially planned as 80-gun ships, but the first two ships built to the design, HMS "Agamemnon" and "James Watt", were rerated on 26 March 1851 to 91 guns ships, later followed by the remainder of the class.

HMS Holderness: Two ships of the Royal Navy have been named HMS "Holderness".  They were "Hunt-class" ships of different periods, named after the Holderness Hunt which operates in the Holderness area of Yorkshire.

HMS King George V: Two ships of the Royal Navy have been named HMS "King George V", after George V, King of the United Kingdom, whilst another was planned:

HMS Amfitrite (1804): HMS "Amfitrite was a 38-gun fifth-rate frigate of the Royal Navy.  She had previously served with the Spanish Navy before she was captured during the Napoleonic Wars and commissioned into the Royal Navy.  The Admiralty renamed her HMS "Blanche after she had spent just over a year as "Amfitrite".  She was the only ship in the Navy to bear this specific name, though a number of other ships used the conventional English spelling and were named HMS "Amphitrite".  Her most notable feat was her capture of "Guerriere" in 1806.  "Blanche" was wrecked in 1807.

Leonidas I: Leonidas I ( or ; Doric Λεωνίδᾱς , "Leōnídās "; Ionic and Attic Greek: Λεωνίδης , "Leōnídēs ", ] ; "son of the lion"; died 11 August 480 BC) was a warrior king of the Greek city-state of Sparta.  He was the husband of Gorgo, the daughter of Cleomenes I of Sparta and the 17th of the Agiad line; a dynasty which claimed descent from the mythological demigod Heracles.  Leonidas had a notable participation in the Second Persian War, where he led the allied Greek forces to a last stand at the Battle of Thermopylae (480 BC) while attempting to defend the pass from the invading Persian army.

HMS Viking: Two ships of the Royal Navy have been named HMS "Viking", after the Vikings, whilst another "Viking" was in service with the Royal New Zealand Navy:

HMS Leonidas: Two ships of the Royal Navy have been named HMS "Leonidas" after Leonidas I, king of ancient Sparta.

Supporting paragraphs: HMS Leonidas Leonidas I
Answer: Sparta