Egypt
Why go? Egypt's tourism has been hammered since the 2011 revolution and the instability that followed, with many tourists and tour operators abandoning Cairo. The main tourist sites, including the Pyramids and Luxor, are more or less deserted. While Cairo and parts of the Sinai peninsula, particularly the north, should probably be avoided, it is still possible to visit the southern Sinai beach resorts.
What the Foreign and Commonwealth Office says: Advises against all travel to some parts of the country, especially North Sinai, because of the significant increase in criminal activity and recent terrorist attacks on police and security forces that have resulted in deaths. In the governorate of South Sinai, the FCO advises against all but essential travel, with the exception of the Red Sea resorts. The FCO does not advise against the use of Cairo airport as a transit stop, provided you do not leave the airport grounds.
Who goes there? Mainstream tour operators are still selling packages to the Red Sea riviera. See Thomas Cook, First Choice and Kuoni. Regal Diving offers trips to more than 10 resorts: relatively undiscovered Safaga is a good spot for novice divers, with its sheltered spots. A holiday costs £507pp, including flights and half-board at the Menaville Hotel.
Read more: On a trip to Cairo, Anissa Helou learns how to make perfect koshari; and how blind writer Ryan Knighton coped in hectic Cairo on a post-Arab spring visit.
Afghanistan
Why go? Highlights include the city of Herat and its 800-year-old Friday mosque; breathtaking lakes at Band-e Amir; and Bamiyan, site of the monumental sixth-century Buddhas destroyed by the Taliban in 2001. Today, only the recesses of the Buddhas remain, but it is still possible to visit the monks' caves and the passages that connect them.
What the FCO says: High threat from terrorism and kidnapping. Advises against all travel to much of the country; and all but essential travel to Kabul, Bamiyan, Parwan, Panjshir and parts of Herat province.
Who goes there? Wild Frontiers, an adventure tour company which started in 2002 with tours to the Hindu Kush, offers three tours of the country, including a 14-day Afghan Explorer (£4,750 land-only), which takes in Bamiyan and the lakes. The website warns: "Anyone wishing to travel to Afghanistan must understand that in places tourist infrastructure is almost non-existent. Days can be long and hard, and the levels of services will not match those offered in more regular tourist locations. However, don't let this put you off. In our opinion, Afghanistan is simply the most fascinating country in the world."
Read more: skiing in Afghanistan
Iraq
Why go? Iraq is defined by its recent troubled history, but it has a 10,000-year cultural heritage, and offers visitors the chance to immerse themselves in the stories and sites of some of the oldest civilisations in the world. Highlights include the Unesco-recognised Hatra ruins, believed to be the ancient lost city of Tayyab; the great Ziggurat of Ur, a massive, stepped structure built in 21BC and restored in 6BC; and Babylon, once the capital of ancient Mesopotamia, and the site of Nebuchadnezzar's palace.
What the FCO says: High risk of terrorism and kidnapping. Advises against all but essential travel to Iraq, except the Kurdistan region. Those who do travel should employ a professional security company.
Who goes there? Adventure tour operator Hinterland Travel (01484 719549) has been operating in and around Iraq for 30 years, although not during the war. It restarted tours in 2009 and in 2014 is running six, nine or 16-day tours, starting in Baghdad, and taking in Samarra mosque, minaret and palace; Nimrud; the city of Hatra and Babylon; and, on longer tours, the marshes around Basra. Nine-day tours costs £2,050pp, 16 days £2,850pp, both excluding flights and visas.
Director Geoff Hann says: "We respect the FCO [and its advice against travel here], but we think we are knowledgeable and experienced enough. Our groups are looked after by the ministry of tourism, who provide security, and sometimes have a police escort. We haven't had any incidents since going back in 2009."
Read more: skiing in Iraq
Iran
Why go? Home to some of the world's cultural treasures, and boasting spectacular landscapes, Iran hasn't been on the tourist list for a long time. With relations with the west starting to thaw, the Iranian government is taking steps to open up the country to foreigners, overhauling immigration rules and promoting its ancient cities, mosques, gardens and ski resorts.
What the FCO says: Advises against all travel within 100km of the Iran/Afghanistan border, and all but essential travel to the rest of the country.
Who goes there? Surrey-based specialist operator Persian Voyages runs tours to Iran, Uzbekistan and Turkmenistan. It has six dates in 2014 for its Highlights of Iran tour (£2,550 staying in three and four-star hotels, including flights).
Read more: Iran's top 10 tourist destinations; and on the road in rural Iran
Algeria
Why go? From the astonishing Roman ruins of Timgad to the natural splendours of M'zab Valley and the Belzma national park, Algeria has loads to offer the intrepid visitor. With a dazzling array of influences, Algiers itself is also a huge attraction and has some of the best cafes in the Med.
What the FCO says: Advises against any travel into the regions around Algeria's borders, particularly those with Mali and Niger. They also recommend avoiding driving or moving around at night, but coastal areas are pretty safe.
Who goes there? The Traveller (01285 880 931) organises a 10-day Roman Algeria tour led by an archaeological expert and taking in Algiers, Timgad, and Djémila from £2,795pp including international flights. Explore (0844 499 0901) has a 12-night trip to Algeria including Timgad and the Mzab Valley for £1,599 excluding flights.
Democratic Republic of Congo
Why go? At the green heart of Africa lies one of its most interesting and yet untried countries. The Congo river is a big draw, as are the gorillas and volcanoes in the east. Access to these, however, comes and goes with the political situation. The north and north-eastern areas are plagued by warlords and extreme violence.
What the FCO says: Advises against all travel to the eastern and northern DCR (except Bukavu), and all but essential travel to the rest of the country, and also points out that street robbery and violence are common throughout the country.
Who goes there? Wild Frontiers runs a 28-day river journey through the Congo, travelling 1,000km of river and venturing into forests and to visit pygmy tribes. The trip costs £5,995pp excluding flights. Steppes Travel has a "land of the bonobos" wildlife tour of the Congo, led by primatologists Sally Coxe and Michael Huxley from £8,995pp, excluding international flights. Luxury camp operator Wilderness Safaris opened two forest camps in Odzala-Kokoua National Park in the remote north in 2012. Located in the Congo Basin, the world's second largest expanse of tropical rainforest, the area is home to Africa's densest population of western lowland gorillas. It's also the richest area in Africa for primates.
Read more: Canoeing the Congo
Georgia
Why go? On the southern slopes of the Caucasus, Georgia has a unique and ancient place in human culture, with its mix of European, Middle Eastern and central Asian influences. There really is nowhere quite like it, from the old hammams of Tbilisi to the magical watchtowers of the Tusheti mountains.
What the FCO says: Advises against visiting South Ossetia and Abkhazia, and also mentions unexploded ordnance from Russia's 2008 invasion. Otherwise, the problems of Georgia are really those age-old traveller woes: roads that get washed away, lack of available horses, and the extreme danger of being inveigled into an all-night drinking and dancing session.
Who goes there? Wild Frontiers offers a number of excellent trips into the country on foot and on horseback. One is the nine-day wild walk through Svaneti region for £1,360pp excluding flights.
Read more: Horse-riding in Georgia
Mexico
Why go? It's a country packed with fascinating cultural highlights. The architecture, music, cuisine and festivals are sufficient to power several years of travel. Then there are the ancient sites, such as Chichen Itza, Palenque and Tulum, plus the vast and energetic capital city with its astonishing street food. But drug-related abductions and murders in Acapulco and along the US border have had a negative impact on tourism recently.
What the FCO says: Reading the FCO advice can be a sobering experience for Mexico, referencing drug-related violence, shopping mall shoot-outs, kidnappings and car-jackings.
Who goes there? Vast numbers of travellers go to Mexico, undettered by bad press, and report no trouble. The Pacific coast, Baja California, the Yucatán and Mexico City are still aspirational destinations for many, with plenty of high-end hotels (see i-escape.com). In the less-visited north, try an authentic Mexican ranch experience from $149 a night with tierrachamahuaecoadventures.com.
Read more: DBC Pierre walks across Mexico City;the best street food in Mexico City; and one woman's journey around the country with a troupe of street performers
Haiti
Why go? There are a lot of reasons to visit Haiti and some strong reasons not to. Despite the endemic poverty, Haiti has a unique and vibrant culture. Away from the earthquake-devastated areas of the capital, Port au Prince, the countryside has steeply – and still sometimes lushly wooded slopes – with impressive waterfalls, including the Bassin-Bleu and virgin beaches. The country has struggled to recover from the 2010 earthquake and even before then, finding off-the-beaten-track accommodation was a struggle. Haiti is not for the faint of heart. Areas of Port au Prince have a serious crime problem, food and water hygiene is an issue, and driving is hazardous. The capital's most famous hotel the Olofsson, a gorgeous colonial building, is still in business, run by Richard Morse, whose mizik rasin band RAM is one of the country's best-known cultural exports.
What the FCO says: Advises against all travel to the Carrefour, Cité Soleil, Martissant and Bel Air neighbourhoods in Port-au-Prince due to the risk of crime. Great care is needed in face of the risk of criminal activity throughout the country. It also notes health risks from cholera and dengue fever.
Who goes there? Very few tourists visit Haiti and most of those who do disembark cruise ships for a few hours on a fenced-in beach. According to a report in Caribbean Journal, the government is looking to develop low-density and sustainable tourism. A new offshore airport is being built on Ile à Vache in the drive to increase tourism. The hope is that funds from tourism will help improve infrastructure and create jobs. Expedia has three packages, all based at hotels in Port-au-Prince. Six nights at the three-star La Maison hotel costs £801 per person, including flights with American Airlines.
Pakistan
Why go? Speak to those in the know and Pakistan often comes out tops. With stunning scenery and an incredible history, Pakistan is a little-visited gem. Some areas and cities are off limits, and care is always needed, but there is so much more. There are World Heritage sites, such as Taxila and Mohenjo-Daro, plus landscapes including the Fairy Meadows and the epic Karakoram Highway through to China.
What the FCO says: Vast areas of Pakistan are pretty much inaccessible for political reasons and the FCO advises against all travel to many provinces. Other areas get a guarded "all but essential travel" advisory, but that still leaves room for exploration.
Who goes there? Wild Frontiers founder Johnny Bealby is passionate about Pakistan, calling it his "spiritual home". He has run countless trips to the region. Group tours start at £1,995pp for a 12-day trip, but the company can also arrange a bespoke tour. Steppes Travel can tailor trips to Pakistan, taking in the Karakoram Highway, Chitral, the Kalash valley and Lahore.
Read more: Howard Marks returns to the borderlands of Pakistan and Afghanistan; a tour of Pakistan's Punjab
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