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Built 1853, the Corn Exchange (which runs through to High St) has been refurbished as a museum.
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The palace is an imposing 1702 sandstone mansion which replaced an earlier castle; you can admire from outside but can't visit within. It's owned by the Dukes of Buccleuch but leased long-term to the University of Wisconsin as a study centre. You can visit the surrounding country park free daily 7AM-7PM, but "Fort Douglas" is an adventure park which, ominously, is demand-priced, and costs more for children than for adults.
Lady Victoria Colliery
Museum set in a colliery, active 1891-1981. An ex-miner takes you down the pit to the coal-face.