We went in April---northern light colors were fantastic and naturally bright green to purple. We stayed at a BNB in old town off the main square and an easy walk to the fishing docks. Daughter did the dive to see the tectonic plates and she would do that again. Make sure you book the Blue Lagoon WEEKS in advance as it fills quickly due to limited entrances to minimize crowding. Nothing organized on our trip and I would also suggest to minimize the group tours and drive it yourself. This allowed us to get to the waterfalls off peak--much better experience. Iceland is getting very crowded and your travel month is in peak season.
Stop and say hi to the Icelandic horses!!
Have a great trip.
J8Tg
Littleton, CO