Was in Reykjavik in June one year. It was cold, light and stunk. The cost of food was high.
But 21 hours of light in summer. :)
Also northern lights should be spectacular.
IIRC it's actually the extended light which drives people to suicide there.
That does not offset it at all. Unless you've got a ridiculously strong character, or a group of friends that will force you to do something with them, I wouldn't recommend it. Or at least have a backup plan if you start going crazy by November.