Depends on what you consider exotic. If it is determined by places few people have visited, I have been up the Noatak River in northwest Alaska to visit a musher who operated a fish hatchery there while we were looking for caribou.
I agree with @Don Alaska what is exotic? Places or things that are exotic for some people, for example the Alaskan wilderness would be commonplace for others. I’ve visited several exotic places at home and abroad but if I had to choose then it would be North Cape in Norway which we visited with my husband’s Australian cousins and watched the midnight sun as it dipped and then rose again without going below the horizon.
I spent a little time in Libya when they had a king, so before Qaddafi, when I was in the Air Force. Driving through Tripoli was an experience of new sights but mostly smells. At a firing range for fighter planes in the desert, we were approached by a Land Rover with no top by a bunch of men who were just being friendly and curious. We bantered as best we could and gave them some American cigarettes and they went on their way. Today we would be killed.
Well, one place we visited, by Carnival Cruise Line, was definitely exotic...........Blackbeard's Island in the Bahamas. Other place, not exotic at all, Yellowstone National Park in Wyoming.
See, that is just my point. To someone form the Cook Islands, the Bahamas wouldn't be "exotic" at all, but Yellowstone might well be.
I've been to the island of Martinique, which was nice (and the only trip like that I've taken), but have fonder memories of the soft white beaches at Muskegon Park on Lake Michigan. Martinique is 1/2 French and 1/2 Dutch, and I happened to be there on Bastille Day. The French Club Med folks were crazy. Back in the 60s we vacationed across a narrow inlet from Assateague Island, just outside of Ocean City MD. Assateague and her sister island Chincoteague are the home of feral horses that are a breed unique to those islands. It is believed that that they descend from stock released on the island in the 1600s by colonists in an effort to escape livestock laws and taxes on the mainland. We would be on the island all by ourselves, and the horses would come almost within petting distance of you, then turn around and walk away. During near-hurricane storms, we stood at the campground looking over at the island, and could see the swell of the Atlantic rise above the horizon of the island. I've been wade fishing many times in the Shenandoah River, getting up to my chest in water pre-dawn with the mist 10 feet over my head--fishing blind--then being in the middle of it as the mist slowly burned off while the sun rose. I think that might be the most exotic place I've been, because I was actually part of it.
My Australia has some exotic places up in our north.. the Whitsundays for example. Breathtaking and exotic but a touch tarnished by commercialism. So I will say the Greek Island of Corfu which back in the early 80s was a veritable exotic but isolated paradise. For instance some of Corfu's beaches were only accessible by a donkey track. One such beach was Perekis in the south of the island. What the little brochure we procured in the town centre neglected to mention was that Perekis was clothing optional. So when we finally scampered down the track to view the most astonishingly clear, turquoise stretch of water we were also confronted by hundreds of people swimming, sunbaking totally au naturale. Now I am not a prude nor am I an exhibitionist.. needless to say it took me several days before I had the cheek to shed my attire.