If possible, as soon as you can! Summer is high season for Iceland so to give yourself the most options, we would recommend booking your flights and accommodations as soon as you are able to! Google flights has a great feature that allows you to track flights for specific dates! https://www.google.com/travel/flights
Average temperature is around 50°F (10°C), but can range from 43-77°F (6-25°C). There is 22 hours of sunlight in June, but the weather can be unpredictable so please plan on bringing layers and rain gear!
So many options for all types of travelers! We recommend visiting this website for general Iceland travel tips and recommendations for things to do! https://travefy.com/trip/6yw9rqkwvyxsqz2addw9lhrhnwfstrq
Your presence enough is a gift!