Yeah, apparently the very high season is crowded to the point of being irritating. And the weather may be bad at any time. However as you’ll be wanting to see the land, don’t go during (Northern) winter as many of the roads can become non-passable, even the Highway 1 may be closed due to ice.
We went in late June (had a stopover in Reykjavik on the way from Helsinki to Toronto) and were warned that it’s going to be very crowded but it wasn’t too bad. There were people at all of the sights that are close to Reykjavik, and often you had to wait a bit to get a photo without anyone in it, but still it was ok. Of course only as we took it to be sightseeing rather than hiking - not much of a wilderness feel at the popular sites. But it’s great that so many of the really great places are so close to Reykjavik- you get to see a lot even in one day. Nevertheless we’d love to go back and I think we will, perhaps early June next time, or end of May if we go without the kids (school summer break starts at end of May or early June).
August and late July are right out, those are the times when most Europeans have holiday and it’s not the best time to travel anywhere in Europe if you have the choice. In Finland schools start again in mid-August so it’s suddenly much quieter but it also means that some summer places close already around then.
