Icelandair hotel Akureyri:
Keahotels.is: Reservation by e-mail to email@example.com. Please state that you are here for the chess tournament.
Amma Guesthouse, https://ammaguest.is/ Single room IKR 90.000 (approx. 700€) for the whole tournament. Reservation through tournament director at firstname.lastname@example.org. Also double rooms and family room, depending on availability.
Our Guesthouse, https://ourguesthouse.is/ Same price for single room as Amma and reserved in the same way.
Additionally, there are several hotels and guesthouses in the vicinity that can be booked on booking.com. Airbnb accommodation also available.