A circumnavigation of Arran should we well within the capabilities of a reasonably fit 13 year old. Just take it easy, have plenty of ice cream or bakery or seal watching stops ...
A word of warning, if you are thinking of doing this during a weekend, make sure you have your accommodation booked! We were once were lucky to find a room, with apparently 3 weddings on the island at the time ....
As someone has said, don't underestimate the southern part between Brodick & Blackwaterfoot, there are plenty of ups & downs, whereas the roads along the west & east coast of Arran are more or less flat. The northern end just has one long climb, but it's not too steep. I've always gone round clock-wise, and would probably stay near Blackwaterfoot if you can find a room there (highly recommend the Lochside Guesthouse just south of BWF if you can get in!), and spend the spare time in the afternoon either walking along the beach towards the King's Cave (look out for otters) and/or drop off the bags at the accommodation and cycle up the road to the small car park for the Machrie Moor standing stones and stretch your legs.
Why do I suddenly feel all nostalgic and want to go back there soon?
Another option for those not sure about hills is the
Isle of Bute, which is much flatter and also has plenty to see & do, and very quiet roads. There are quite a few loops or out & backs that can be done from the town of Rothesay. You can drop your overnight stuff off at a B&B and then just travel lightly for day trips (there is a write-up on our 2.5 day tour of Bute last May on the same blog I mentioned earlier). Bute is just as easy to get to as Arran by public transport, with plenty of space for bikes on the train & ferry. I love cycling down the ramp onto a ferry, that's when the adventure begins ...
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