Scone - scone
The pronunciation of the name of the item of bakery - the little cake of flour and butter - associated with Scotland is an in-group marker. Some pronounce it in the traditional way, to rhyme with 'gone', IPA: /skɒn/. This is the preference of 65% of British speakers in a 1998 poll in LPD. Others regard it as more refined to make it rhyme with 'alone', IPA: /skəʊn/, which the older generation in Scotland reject. (It is the dominant pronunciation in America.) OED (1910) recorded the pronunciation rhyming with 'alone' as the first pronunciation, implying that it was then the majority choice, although its sampling may not have been as thorough as that of LPD (2000).
The ancient town in Scotland, where King Robert the Bruce and Macbeth, amongst others, were crowned, is spelled the same way but pronounced to rhyme with 'soon', IPA: /skuːn/. This is the pronunciation for 'the Stone of Scone', the traditional stone on which Kings of Scotland were crowned. It was taken to England by Edward I, and built into the Coronation Chair in Westminster Abbey. So Kings of Scotland were still crowned on it. It was transferred to Edinburgh Castle in 1996.
The food item does not take its name from the town, or the Palace. It is "perh[aps] a shortening of MLG. schonbrot, MDu. schoonbrot 'fine bread'" (CODEE).