The McManus is Dundee's main museum and art gallery, housed in a confident 1860s Gothic-revival building by Sir George Gilbert Scott. The collection is broader than you would expect for a city of this size: Scottish art from the eighteenth century onwards (including Pre-Raphaelites and the Glasgow Boys), Pictish stones, a strong natural history section, and Egyptian antiquities collected by Dundee jute merchants who travelled the world.
The galleries on the city's industrial heritage — jute, whaling, shipbuilding — are particularly good. Free admission. Allow at least two hours.