Rainy in Iceland?

Most likely you would get a mixture of different kinds of summer weather: rain, sun, warm, cool, etc., but you never know. Icelandic weather is hard to predict a day in advance, let alone a year. It's always a lottery, but choosing July/August will increase your chances of experiencing really good, warm weather. It's hard to be more precise than that.

What will the weather be when you go - who can say? It is weather, and it is variable. All we can do is look at the statistics, and recognise that something different might happen when we turn up. Dry spells of a week or two do occur, but probably not every year, and their precise dates cannot be predicted. But, in contrast to New Zealand, the rain is mostly fairly light, and it doesn't rain all day too often.

Reykjavik is probably a fairly typical location in terms of rain: there is both rather wetter and rather drier. The east and north of the country is drier than the rest, (excluding the NW) especially the NE interior (Myvatn etc). July is drier than either June or August. But it still rains fairly frequently, wherever and whenever.

The driest month is actually May, but it tends to be still rather cold then: heavy snowfalls are still possible in May, though not particularly common. The same can be said of late August.

Thank you all for your responses, it's much appreciate. I look forward to my visit.

Yes, Iceland's weather is notoriously capricious. You kind of have to take your chances. The east of Iceland can be a little calmer and warmer in the Summer months...