Are you as well travelled as the Queen? The countries you should visit that she hasn't

For obvious reasons the Queen has never visited Argentina (though Prince Philip did visit alone in 1962). Indeed, with little historic or political ties to the continent - excluding Guyana and the Falkland Islands - trips to South America have been few and far between. She travelled to Brazil and Chile in 1968, and to Guyana in 1966 (when it was still British Guiana) and 1994, but has never been to Argentina, Peru, Colombia, Ecuador, Uruguay, Bolivia, Venezuela, Suriname, Paraguay or French Guiana.

Greece

The Queen did visit Greece in 1950, before she became Queen, but has never made a state visit to the country. It's an interesting omission, particularly given the fact that her husband was a Greek prince born in Corfu. However, as viewers of The Crown will be aware, his relationship with the country is an unhappy one. Prince Philip's father, Prince Andrew of Greece, was put on trial in 1922 after a Greek military defeat, almost executed, and the entire family - including an infant Philip - was forced into exile. The Duke of Edinburgh has returned occasionally, but always alone.

Costa Rica

As with South America, there are few colonial ties between Britain and Central America - Belize, and parts of the Caribbean coasts of Nicaragua and Honduras, excepted.

Which explains why the Queen hasn't visited Costa Rica, the world's happiest country and heaven for wildlife lovers, Panama, Nicaragua, Honduras, Guatemala or El Salvador.

Israel

There are obvious reasons why neither Israel nor the Palestinian territories have welcomed the Queen. Security is a major factor. The Foreign Office must approve all state visits, and its advice for ordinary travellers to the region, let alone high-profile ones, is packed with warnings and caveats. Then there is the diplomatic sensitivity over visiting Jerusalem, which both Israelis and Palestinians consider their capital. The Queen is always keen to avoid getting embroiled in political matters.

Other Middle Eastern countries The Queen hasn't visited include Iraq, Syria (both unsafe to visit, according to the Foreign Office) and Lebanon.

Albania

There's a fair chunk of Europe yet to receive a state visit from The Queen, mostly minnows and former members of the Soviet Bloc. If you've been to Albania, one of Europe's best-kept travel secrets (and, according to some, a rival to Amalfi Coast), Liechtenstein, Andorra, Belarus, Bosnia and Herzegovina, Bulgaria, Moldova, Ukraine, Macedonia, Montenegro, Armenia, Georgia or Monaco, you can claim minor bragging rights. Kosovo, too, has not been visited - largely because it didn't exist before 2008.

Note that The Queen has not been to the modern states of Croatia or Serbia, but did visit Dubrovnik, Belgrade and Zagreb in 1972 as a guest of Tito, the 20th century's least objectionable communist dictator.

Cuba

Most of the Caribbean has been ticked off, but not all of it. The French overseas territories of Guadeloupe and Martinique, for example. The US Virgin Islands and Puerto Rico. Haiti and the Dominican Republic. And also Cuba. Again, political and security considerations will have played a part. What has she missed out on? "The Caribbean's most fascinating country," according to our expert, Fred Mawer. "A heady mix of faded Spanish colonial cities, sputtering Fifties Cadillacs, wonderful live music, world-class cigars and an arcane communist system."

São Tomé and Príncipe

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When it comes to Africa and the Indian Ocean, most current or former Commonwealth members have received the British head of state. South Africa, Zambia, Zimbabwe, Mozambique, Kenya, The Gambia, Ghana, Namibia, Nigeria, Seychelles, Malawi, Uganda, Sierra Leone, Mauritius and Tanzania all make the list.

But several don't, namely Rwanda, Cameroon and Lesotho.

The Queen has never visited Egypt, either, an omission that might owe something to security concerns and something to the Suez Crisis of 1956. Other destinations not seen by The Queen include Libya, Mauritania, Senegal, Mali, Guinea, Guinea-Bissau, Ivory Coast, Burkina Faso, Chad, Cape Verde, Comoros, Central African Republic, Gabon, Congo, the DRC, Angola, Burundi, Swaziland, Djibouti, Somalia, Togo, Benin, Equatorial Guinea, South Sudan, Eritrea, Mayotte, Niger, Reunion and… São Tomé and Príncipe. If she ticks off just one, we'd suggest making it this. According to John Gimlette, who visited recently for Telegraph Travel, they are the paradise islands that tourism forgot.

"It's easy to see how you might overlook it," he says. "When I first spotted it on a relief map of the Atlantic, it looked like two needles rising off the ocean floor, each with a tiny island perched on top. São Tomé is roughly the size of Anglesey, while Príncipe compares to the Isle of Wight. Separated by 99 miles of ocean, they are, in cartological terms, a pair of free-floating full-stops.

"Closer up, they're harder to ignore. From the air, they look improbably dramatic. Having risen 3,000m (9,840ft) off the seabed, parts of them carry on rising another 2,000m (6,560ft). There's nothing undulating about these mountains. They're like great blue fangs, covered in a rich velvet of forest and cloud. One of these peaks – on Príncipe – is so sheer that, until recently, it was thought it had only ever been climbed twice in 31  million years. It's ridiculous to describe anywhere as a Lost World now, but this one got seriously mislaid."

Madagascar

Our monarch has also never been to Madagascar. The island is famous for its lemurs and chameleons, while fans of the Flashman novels will know it for its "mad" 19th century queen, Ranavalona. She thwarted European efforts to gain sway over Madagascar during her 33-year rule, but also focused her energies on brutally eradicating Christians, neighbouring kingdoms and political rivals. So widespread were the purges, and the use of slave labour to construct a vast palace and public works, that the island's population fell from five million to 2.5 million between 1833 and 1839. One way Ranavalona maintained order was the tangena ordeal, by which the accused was poisoned, and then forced to eat three pieces of chicken skin. Death, or the failure to regurgitate all three pieces, indicated guilt. Others opponents were simply thrown into vast ravines. The remains of her palace, the Rova of Antananarivo, can still be seen in the capital. A possible stop on any unlikely future royal tour.

Mongolia

The world's least crowded country is one of 16 Asian nations never to have welcomed The Queen (the others are Bhutan, Uzbekistan, Kazakhstan, Turkmenistan, Afghanistan, Tajikistan, Kyrgyzstan, Azerbaijan, Myanmar, Vietnam, Cambodia, Philippines, Timor-Leste, North Korea - obviously - and Laos).

It really is perfect is you like peace and quiet. Terry Richardson visited for Telegraph Travel last year. "This enormous landlocked country of green steppe, vast flat plains, intricately braided rivers, electric-blue highland lakes, snow-licked mountains, dense pine forests and shifting desert is presided over by a skyscape of such bold blue immensity it beggars description. It's not just vast; Mongolia is empty, too. Three times bigger than France, its population is less than a 20th of the UK's – and one in three people live in the nation's sole city, the capital Ulaan Baatar."

Palau

The Queen has seen more of the South Pacific than you'd care to mention. The Royal Yacht Britannia, decommissioned in 1997, enabled her to island hop in far-flung corners of the world with relative ease (for most ordinary travellers, a cruise ship is the way to go). But we've uncovered four missing pieces to this paradisiac puzzle: Niue, the Marshall Islands, the Federated States of Micronesia, and Palau. The last of these probably has the most to offer. It is pure Bounty advert territory, with pristine beaches, world-class scuba diving, and forest-covered volcanic islands.

So where does she go to relax?

These aren't holidays, of course. They are working trips, filled with mundane sightseeing and dull dinners with dignitaries. So where does The Queen go to unwind? The Bahamas? Sardinia? Tuscany with the corgis? Of course not. "The Queen doesn't have holidays," Hugo Vickers, a royal historian, told the BBC back in 2012. "She goes to Balmoral."