16 hours, half of which will be sleeping and the other half exploring. If I get my bag do I need to recheck it on return? Is there another fee? Where would it stay at KEF if I can't grab it?
Definitely questions for your airline
I'm a former airline employee. For any layover that long I would DEFINITELY claim my bag and re-check it for the second flight. There are too many problems with airline baggage theft and this is a prime example. Don't let your bag sit that long in a holding area, too big a temptation.
I had a 10 hour layover and just checked my bag all the way through. I had no difficulty. There is a hotel near the airport that will provide left luggage service if you feel you must claim your bag.
As suggested above, verify with your airline. Some have limits as what they consider a connection vs a layover or stop, either automatically checking it through vs dumping onto baggage check. Additionally, you may be able to request picking up your bag or request they keep it.