We would be tempted to say that the best time to travel to Iceland would be in June, July and August but there is no best time actually. Everything depends on what you are looking for. Iceland in summer time and Iceland in winter time is two different countries.
In the summer time you have the day light 24h/24h, that is magic. You can cross the country from south to north or vise versa by the highlands. You will see incredible colors in the highlands - you can rent a car and then visit