Best time to visit Iceland is July and August and worst is January - March from climate point of view. Well you can visit in June, and up to 15 September everything shuts after that, though December is lively in Reykjavik.
Minimum worthwhile stay including a quick whizz around the Golden Triangle is one week and also include a weekend for a taste of the nightlife.
Third Thursday in April is the First Day of Summer with Sumardagurinn Fyrsti, mild partying and a carnival in Reykjavik. First week in June is Sailor's Day called Sjomannadagurinn, watery competitions and partying in coastal villages.
Beginning of August is with Verslunarmannahelgi, camp based partying in Iceland's car accessible scenic spots; extreme drinking and mayhem.