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I can't think of anything worse (OK I can) than riding on Route 1. Endless brutal wind and tourists wizzing by on a narrow road at 80kph. Did they ride in the night to get pictures of empty roads?! Think that's the only way I'd do it, middle of summer but flip the time and ride in the 'night'.
Do really want to go back and ride through the middle though.
https://bikepacking.com/routes/iceland-divide/
We went to the capital in December years ago.
https://www.tripadvisor.co.uk/Hotel_Review-g189970-d619115-Reviews-CenterHotel_Thingholt-Reykjavik_Capital_Region.html
It was quiet and nice. Maybe it depends what time of year? Maybe it's just got busy?
https://cyclingtips.com/2015/10/roadtripping-iceland/