We went to the Azores one summer, think it was July. Absolutely gorgeous. Spent one week on ponta delgada, followed by a week on terceira. Short flight, between them. We flew from Manchester via London and onto the Azores. I am not a sun worshipper, struggle in high temps, so have been to quite a few 'moderate climates'. The Azores was a real mixed bunch weather wise. I remember sitting on a black volcanic beach with a towel over my head, there was no cover and I was afraid of being burnt. Plenty of days, really warm and mild, low 20's. on terceira there are warm volcanic rock pools to swim in, so even when cool the water was great to swim in. Hmmm memories, I want to go back! Went whale watching, saw one leap out of the water, loads of dolphins all round the boat.
Other possibilities we have tried
Iceland in July, great holiday, IMO best for active pursuits, was quite chilly at times, and very windy. No rain.
Norway in July - great destination, gorgeous scenery, we were a bit unlucky with weather, rained a lot.
Corsica in September. Still very hot (30's) first 2 weeks, then starts to cool down quite rapidly last 2 weeks. We went last 2, first week perfect temp for us in the high 20's, last week much cooler with some rain. A local told us, their weather is very predictable and changes abruptly like this every year.
Nova Scotia - Canada . Best holiday ever, jaw dropping scenery, lots of activities, kayaking, river rafting etc. went June/July, not to hot in the 20's. perfect weather for getting out and about in. Think temps would be good in August, it's northern and coastal.
Finland, last 2 weeks in August. First week, lovely weather, sunny, no rain, low 20's. 2nd week, autumn arrived with a vengeance. On the last day of hol 31 st aug, we got up and there was ice on the car, had to de scrape before driving to airport. All the tourist stuff started to close in our 2nd week as their summer season was ending. Good holiday though, stayed one night in a bear hide and watched a mother bear and her cubs amble past. Unforgettable but chilly!
Hope this helps