From Glasgow, two options – Follow the cycle route that goes out through paisley, johnstone, lochwinnoch down through Kilwinning and Troon and into Ayr. It’s then only about 8 miles on the road out to Dunure.
Other option is out to Newton mearns and down the old A77 which has been converted to a cycle route, down to Fenwick, then takee country roads to symington, monkton, Prestwick and into Ayr.
1st option is longer but flatter, 2nd more direct but a bit lumpier.
Dunure is a stunning wee place, a favourite of ours for a wee impromptu sausage sizzle on the beach. Post up when yer going, if I’m about I’ll get the coffee on when your coming through Prestwick.
From Dunure head for old dailly, then straiton and the Glentrool road. It’s a belter of a road, and has been resurfaced over winter, like a bowling green.
If you want I can make a GPX of the Galasgow to Dunure route for you.