Yes! The majority of hotel room reservations are fully refundable as long as you cancel prior to the hotel's cancellation deadline, which in most cases is within 24 or 48 hours of check in. If your reservation is non-refundable, you might be able to cancel it and get a refund within a 24-hour period of booking. Put your dates in and click on "Search", then you can filter by "fully refundable" to get the best options available near Reykjavik University.