Ayrshire faces west across the Firth of Clyde towards Arran and, on clear days, Northern Ireland. It's primarily known for two things — Robert Burns and golf — and while that sounds like a narrow brief, both run deep enough here to sustain serious interest.
Burns was born in Alloway near Ayr in 1759 and spent most of his life in Ayrshire. He's taken seriously here rather than just commemorated, and the landscape he wrote about — the farms, the River Doon, the roads between the towns — is still recognisable. The Burns Birthplace Museum in Alloway is the main site and is well done; the Brig o' Doon and the ruined auld kirk next to it are nearby.
Ayr is the main town — a decent market town and seaside resort with a racecourse and a long beach. It's unpretentious and functional. Troon to the north is smaller and quieter, organised largely around its golf course. Royal Troon hosts The Open on a rotation; the course is links, exposed and technical. Prestwick, just south of Ayr, hosted the first Open Championship in 1860 and is an interesting course with genuine history attached. Turnberry on the south coast is the most scenically located of the lot — the lighthouse and the view of Ailsa Craig from the fairways are hard to beat.
Culzean Castle, south of Ayr on the clifftop, is the most visited National Trust for Scotland property and the Robert Adam building is the reason why. The cliff setting is dramatic, the grounds are extensive and the whole estate is a good half-day. The views from the castle's round drawing room over the Firth of Clyde are the best bit.
The Isle of Arran is reached by ferry from Ardrossan — about an hour crossing. The island has a north-south split: northern half is mountainous with Goat Fell (874m) as the highest point, southern half is gentler farmland. It has its own distillery, its own cheese producer, and enough to occupy two or three days without difficulty. It gets described as Scotland in miniature, which is a bit of a cliché but not entirely wrong.
Kilmarnock is an inland town with limited visitor appeal but an important place in Burns history as where his poems were first published. Largs on the Clyde coast has a pleasantly old-fashioned seaside feel and good ferry access to Great Cumbrae. West Kilbride has reinvented itself as a craft town with independent shops.