Donegal Town is a fairytale of a place, featuring a charming harbour, serene beaches and stoic stone remains of centuries past, like those of 15th-century Donegal Abbey. Stern-looking Donegal Castle, recently restored to its one-time Gaelic glory, is the crown jewel of the area. If you’re looking for souvenirs, snag a hand-woven tweed or carpet, the signature goods of the area. For a good craic, the pubs of The Diamond area are a sure bet.

One of southeastern Sicily’s UNESCO-listed baroque cities, Noto is famed for its opulent architecture and surfeit of beauty. Its 18th-century cathedral is a local highlight, as is Caffe Sicilia, which is rumored to make some of the best gelato in all of Italy.

Cairo’s an ancient city that also happens to be a modern metropolis—it’s one of the biggest cities in the Middle East and has the traffic and noise issues to prove it. But as long as you’re not looking for solitude, Cairo—the City of the Thousand Minarets—is a splendid place to explore Egyptian history and culture. (Editor's note: Our list was compiled before political unrest prompted many countries to issue travel warnings for Egypt. If you're currently planning a trip to Egypt, please consider the risks and monitor your government's travel alerts.)

The first time you go to New York, go ahead and be a sight-seer—everyone should visit the Statue of Liberty, the Met, Times Square, etc. But on a return trip, pick a neighbourhood and go deep. You’ll find hole-in-the-wall bars, great delis, quirky shops… exploring the non-touristy side of New York is an incredibly rewarding experience for a traveller.

Laid out by British architect Edwin Lutyens, the Indian capital is a striking modern metropolis. A gracious contrast to Old Delhi's winding streets, the grand avenues and stately buildings of New Delhi are rich with history and culture, from Gandhi's Delhi home (and the site of his assassination) to the tomb of Humayun, a complex of Mughal buildings reminiscent of the Taj Mahal. Chaotic traffic is best left to the locals. Negotiate a good price for taxis or travel on the new Delhi Metro.