... Been twice, the second time to do the Midnight Sun Run in June.

For a short trip, I would highly recommend you hire a car and see the Snaefelness Peninsula. We saw the Lava Cave, drove up to the glacier (a dirt track), had a wee singalong in the Singing Cave, took pics of Kirkujfell, popped into a village hot spring bath (can't remember where exactly) and saw lots of beaches. A special (long) day out.

We avoided most of the touristy places both times. So for instance, try Nautholdsvik Geothermal Beach near the airport rather than the Blue Lagoon. It's around a tenner now. Cooling off in the sea when we went in January after the hot tub was... an experience..

Oh, and we loved the punk museum in the Reykjavík former public toilets... 😊