>"I hear that one can hike right out the door of Reykjavik airport."
True, that. But it is a bit of a moonscape on that SW peninsula that used to be the US base.
But from Keflavik Airport or from Reykjavik city 50 km to the north, you can book bus tours of hot springs, waterfalls, spas, lava-tube caves, and/or horse rides. You could leverage a layover afternoon, a day, or several days if you planned ahead. For how much farther west we need to go back to Alaska, it was really nice to break-up the time shift with several days there. We just rented a car. Driving was much easier with wider lanes, slower speeds, and more politeness than on the continent. Lodging, food and service prices were high (think Switzerland and double the price on produce) but BPing or bicycling would solve that.
We saw an impressive number of people bicycling touring through the national parks. The flights are cheap from Europe and it is Europe's least densely populated country. Sort of like if you 48-staters could pop up to Alaska in 3 hours and for $140. Windy and rainy a lot of the time, the ponchos and goretex seemed kind of pointless. The most experienced people seemed to just resign themselves to being moist all day and had dry-as-your-wear-it synthetics on.