Anyone here live in such a locale and wanna give me the SD? “This place is just too damn sunny and beautiful, I wanna visit somewhere cold and overcast!” 
Perhaps a skiing holiday, or a visit to a big city, with lots of museums, galleries, theatres, etc. Anything to get way from that boring beach
Friends and realitives stop crashing.
Vegas Baby!!
What a great question, really.
I mean when you’re livin’ on sponge cake and watchin’ the sun bake all of them tourists covered in oil, what do you do to get away from it all?
Antarctica.
I don’t, nor have I ever lived on an idyllic tropical island, but I did grow up near the coast, and had both sets of grandparents live on the coast, as well as friends and relatives with beach houses a-plenty. Needless to say, I was at the beach all the time up until college.
I have little use for a beach vacation as a result. My ideas of a dream vacation are neat cultural things and interesting places. Some may have beaches nearby, but that’s not the reason I’d go.
Ice fishing on Lake of the Woods, of course.
New York City is a popular holiday destination for Caribbean islanders.
I went on a trip to Europe when I had just graduated from high school. One of our stops was in a drop-dead-gorgeous Swiss town, with a lovely lake framed by breathtakingly beautiful mountains. Everywhere you looked, it was like a painting. Just sheer glorious nature, and picturesque homes, and lovely shops with excellent food, etc.
In one of those shops, I was trying to speak in my shitty German to the 18-year-old kid who was working the counter. He responded to me in his much-better English and we had a little conversation.
“So do you like living here?” I asked him. And he said, “I can’t wait to move out of here; this town is horrible. It’s so boring and nothing ever happens.”
I suspect it might be much the same for the hypothetical residents of the tropical island.
Go to another sunny and beautiful place, of course. I wouldn’t had move to such a place in the first place if I’d like some other location. 
My GF on the other place likes to elope to snowy places.
We may do internal tourism. 
Meaning, we actually get to relax and enjoy what we have, instead of actually having to work (so that we can afford the time off and vacations).
Also, going to Disney World is very popular.
And there is nothing wrong with visiting other locales, then we realize, our beaches (and food) are better.
But alas, the people I have to be around every day are at those same beaches, and that kinda ruins it 
Like drachillix and Implicit hint at, the tendency would be that if “home” is idyllic(), then “out on holiday” would be wild and exciting.
( A huge if. Tourism Offices do great advertising, don’t they…)
I can’t answer for the Caribbean or Pacific, but “island syndrome” is a well-known phenomenon, a sort of claustrophobia suffered by people who have recently moved to an island and who occasionally get overwhelmed by this feeling of “OMG, the farthest I can drive from my house without taking a ferry is about 100km, aaaaargh!” I imagine it’s more likely to strike someone in Hierro than in Tenerife, simply on account of their relative sizes.
People from the Balearic and Canary Islands take short vacations going shopping to the mainland, and their dream vacations usually don’t include any beaches (well, the ones at home). I understand those from Ibiza don’t normally bother much with going clubbing in Parts Abroad, either…
Interesting thread-many people DON’T like tropical beaches, island sunsets, etc.
One such a man was a friend of my father-he retired to northern Vermont! He liked winter, and hated the bugs and heat of summer-his ideal day was a snow covered landscape, with an ambient temp. about 20 F.
His wife, hated winter (she spent her winters in Florida).
Relevant anecdote: this past summer, I was working in Madrid and we had an Austrian consultant spend several days here. He once asked “so where do Spaniards go on vacation, to gloomy Austria?” Actually… yes, it’s a pretty popular spot for summer vacations, as are Fjords Cruises, Hungary, Scotland and the Czech Republic. Doesn’t mean we don’t go to the Dominican Republic (we sure do), but… why would you fly to Santo Domingo in August? If you want heat in August and you live in Spain, you simply stay home!
I like visiting such places but I certainly wouldn’t want to live there full-time.
I hate the beach. I burn so easily that living in a hot environment was very unpleasant for me growing up and as soon as I could I moved north to get the hell out of the heat. I can imagine that if I had grown up in Hawaii instead of Texas I would still hate the heat and moved somewhere snowy as soon as I got the chance. I am not a big fan of warm weather vacations and I tend to go places with lots of cultural things to do or lots of snow if I’m going to do outdoorsy stuff.
When we got married my husband and I took our honeymoon in Finland in November. We went snow tubing and dog sledding and had a great time. My parents just shake their heads at our weirdness and enjoy their annual trip to Cancun. To each their own!
I lived in San Diego for 5 years.
Naturally I moved to Cleveland, that is my anecdote.
I love it here, and I find beaches boring.
This.
I have a sister and a cousin who live in Hawai’i, and parents who go there for two months every winter (with me occasionally joining them), and I have to say that “Island Syndrome” is very real, even – or maybe especially – among long-term residents.
The cousin flies for Hawaiian Airlines, and tells me that their flights to Las Vegas are packed year 'round.
His fellow islanders, he has told me on more than one occasion, just love to see wide open spaces.