There are no showers in the airport. The only showers you will find are those you get with accomodation (whether hotel, camping, or AirBnB)
Can't answer specifically, but your post caught my attention.
When I fly West, so days are muuuuch longer that the shower thing rung true with me.
After checking that my passport is still in the same place it was the 12 times I checked before, the last thing I do before leaving home is shower.
I've never even considered that showers would be a thing to have at airports. Are any US based airports offering showers ? Or airports anywhere else in world for that matter ?
Yes, Rikki_121 most international airports have shower facilities as well as lounges you can pay for or have access to if you are a member (certain credit cards also allow access)
You can also buy "wilderness wipes" or similar. I usually travel with those anyway since I find planes gross. I feel somewhat clean after rubbing my face or neck with them.
Shows I've never traveled business class 😁😁
Airports IMO tend to be places where I would like to spend as little time in as possible.....
I think stopping at one of the pools FrozenBaz suggested would be your best bet if you have a rental car and can spare the time. Or you could contact Icelandair and ask if you can buy access to the Saga Lounge, although I don't think that is possible. Otherwise you may be out of luck.
I usually also bring wet wipes and some essentials to freshen up on the plane at the end of a long flight.