The Azores were fantastic. We only stayed on Sao Miguel, but there was more to do there than we could manage in a week. The food was fresh and delicious, the natural environs were absolutely stunning (think of a mix between Hawaii and Ireland), the culture was unmolested by Americanism, and everything was so cheap. We did a lot of swimming and hiking. There aren't any mega-hotels or resorts there yet, so that added a layer of pleasantness for us. We stayed in a 3 BR home with a pool for $450 a night. Go now before capitalist pig-dogs ruin it with nasty hotels.
For Hawaii, we stay on Kauai. My best friend moved there in 1994, so we've been around 20X now. Thanks to their generosity with their home (I guess you kind of have to have a guest BR if you live in Hawaii), we've never had to pay for a hotel, which means we generally cook every night. Done that way, Hawaii isn't terribly pricey. And when you get away form the hotels, it becomes a quiet, rural island that's as close to perfect as I can imagine. Hiking, paddling, surfing, snorkeling, and swimming are all near daily activities. Fruits and vegetables grow everywhere, and the fish is abundant and unparalleled, in my experience. The natural beauty is astounding in a way that takes you out of your head and into your senses, which I something I desperately need living in Atlanta.
We've also spent a good bit of time on Maui and Oahu. Strongly prefer Maui to Oahu, but it you head North out of Honolulu, Oahu can be pretty amazing.