Gretna Green.
On the other hand, Portpatrick on the Galloway coast is a delightful village, with pretty cottages around the harbour, and a ruined round-towered medieval church that is Irish in style, It's Ireland's Gretna - eloping couples could get straight off the boat, be hitched and back onboard for the return trip within the hour. I've been there twice, once in my motorbiking days and then on a cycling tour of southern Scotland when we lived in Ayrshire.
Very popular with yachties in and around the Irish Sea and also the start/finish of the Southern Uplands Way.