We landed literally the day after "the season" ended in mid-September, but in no way did that stop us from enjoying this country filled with natural beauty, and the vibrant city of Reykjavik with its music, art and a culinary scene. We were in awe at the constant shifts in weather (you've never seen so many rainbows!) and the diversity of this land. There are many waterfalls to see with relatively easy access including Seljalandfoss, Gulfoss and Skogafoss. Along the south side of the ring road, you'll find Skogafoss lined with black sand where you can walk relatively close to the falls. Here you'll also discover the Skogar Folk Museum where the way of the Vikings is preserved and displayed in a beautiful natural setting.
I highly recommend starting or ending your trip at the natural thermal spa, The Blue Lagoon . You'll have access to clean and well-organized locker rooms, spa scrubs (go to the counter and order the set of 3 for purchase or you can access free mud in the thermal pools. Look for the wooden buckets along the sides), refresh with some Icelandic spring water or you may choose to sip some champagne while soaking in these healthy and steamy pools. It's close to the airport and with the departing flights back to the US leaving in the afternoon, it's a perfect way to wrap up your trip before you travel home.