this is a website that lists elementary schools all over iceland:
this website is an informational website for parents, students, and teachers, so you could try sending them an email (click p贸stur icon on the left near the top).
the other possibility is contacting the ministry of education, who might have some ideas. There are a lot of exchange-type programs with Icelandic teachers who travel to schools in other countries (organized by the ministry) to learn how schools operate elsewhere, so they might have an idea.
keep in mind for both of these links that not much happens in Iceland over the summer, so it might be better to make inquiries in late August rather than now.
