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Photo: Martin Le Roy, CC BY-SA 4.0 via Wikimedia Commons
"Killie" play soccer in the Premiership, Scotland's top tier. Their all-seater home ground is Rugby Park (capacity 18,000), half a mile south of the railway station off Dundonald Rd A759.
Rugby Park, also known as The BBSP Stadium Rugby Park for sponsorship reasons, is a football stadium which is the home of Scottish Premiership club Kilmarnock F.C. and is situated in the Scottish town of Kilmarnock. With a capacity of 15,003, it is the 7th–largest football stadium in Scotland, and was first used in 1899, also having been used for concerts, rugby union and international football fixtures. The stadium underwent a major redevelopment in 1994–1995, becoming an all-seater stadium with a capacity of 18,128. In 2002, the club constructed the Park Hotel, a 4-star hotel complex next to the ground.
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James Dick was born in Kilmarnock; he left for Australia but endowed this civic institute, opened in 1901. There's a museum and gallery.
The first edition of Robert Burns' collected poems was published in Kilmarnock in 1786. Only 612 were printed, so these are prized rarities. The centennary of publication drew support for erecting a monument. It was completed in 1879 with an attached museum, in a grand mixture of every architectural style then known, as the centrepiece of Kay Park. But in 2004 the Burns Centre burned. The surviving parts were incorporated into a new Centre, opened in 2009, which houses the civil Registration Office and local history archives. It was nominated for the Carbuncle Cup, awarded annually to Britain's ugliest new building, for its "forced, clumpy monstrosity with pointlessly random rooves." (It lost out to Strata SE1, a tower block in London Southwark.) The centre isn't a museum, but you might research your Ayrshire ancestors here.
The castle was built in the 14th century but heavily made-over in the 19th. It has a museum and country park.