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On a trip to Iceland I took the bus to my hotel in Reykjavik and put the bike together in my hotel room which was a lot more relaxing. I think getting a hotel is the nicer option rather than a ride immediately after a long flight. You can also either leave your bike bag at the hotel if you are coming back or post it to yourself at a convenient post office. Spending some money on taxis and hotels is worth it if you are lugging a bike around in a bag.
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I took the bus to the hostel next to the Reykjavik campground, stayed there two nights, gave me time to assemble bike (was in an S&S case, so more assembly required), buy a bunch of groceries, pick up some maps, and try to reset myself to a very different time zone.
I know that some on this forum prefer to get off the plane and start riding from the airport. If that works for them, great. But I want a more relaxed time table. I am there to have a good time. That said, I am retired so my trips can last longer with no job waiting for me too soon after I fly home.
That Carradice bag looks REALLY full. I assume that is a camper longlflap?