We fly to Scotland from the Great Smoky Mountains of North Carolina, home to many folks of Scottish descent. There's even a Tartan Museum in Franklin, NC and there are many highlands festivals each year all over these mountains. . . but that's another story!
To get to the Isle of Arran, fly to Glasgow, then rent a car and drive about 40 extremely scenic minutes through verdant, sheep-dotted hills to a coastal town called Ardrossan. Your goal is the Caledonia MacBrayne ferry to Arran. Trains to Ardrossan are also available. Without a car, you may rent a bicycle or ride the buses while on Arran, if you prefer. Caledonia MacBrayne (everyone calls it CalMac) has an astonishing variety of ferries in Scotland, primarily the west coast. They can take you to the famous Isle of Skye, the islands of Mull, Jurra, & Eigg, or the farthest Hebridean islands of Lewis and Harris, among others. Someday I would like to take a month to ferry from island to island.
The ferry to Arran is large, with comfortable deck and lounge areas. I always count on a bowl of Scotch broth and a cup of Earl Grey tea from the ferry restaurant's warm, friendly young staff to comfort my tummy after the long overnight flight. It takes about 55 minutes to cross the Firth of Clyde from Ardrosson to the pier in Arran's main town, Brodick. From the windows, or the deck, you will see the mountains of Arran, Goatfell chief amongst them, begin to appear. Brodick Castle, perched above the coastline, is a further reminder that this is an ancient land, full of history and mystery. You begin to see the storybook village of Corrie, with its tiny rose bedecked cottages almost sitting on the road, a tiny ribbon between them and the Firth. Disembark as soon as you can. Maybe you're in time for sheepdog trials and the country fair at the castle!