The best months to visit the Azores will be July and August. While it is the touristy season, you will have a better chance to experience the most favorable weather conditions. During this time is when the least amount of rainfall hits the islands, so it gives you a better chance to fully experience what the Azores have to offer. And don’t worry - although it is high season, the islands wont be overrun by tourists. I found my time to be quite enjoyable altogether, even during the peak summer months.