From the bustling charm of Galway City to the rugged, otherworldly Burren, Western Ireland offers a wonderful wealth of experiences. Exuberant Galway, City of Tribes, packs summers with festivals and packs pubs with locals and visitors. Westport is another charismatic town, full of colourful shopfronts, pubs and great restaurants. The near-lunar landscape of the Burren delights with its unexpected flora. Don't miss its Stone Age burial monuments, fishing village Ballyvaughan or cheerful Lisdoonvarna.

Tenby is lovingly protected from the outside world by an embrace of 13th-century stone walls, which, ironically, attract—not repel—visitors from all over the world. The town is simply adorable, teeming with the archetypes of pubs and shops one would expect to find in a U.K. city. Adding further appeal are the miles of gorgeous beaches and the gently lapping waves of a blue-grey sea.

Olbia (Greek for “happiness”) is a popular jumping-off point for those visiting the white-sand beaches of the Costa Smeralda, but those who linger in the coastal city uncover a historic centre filled with archaeological landmarks, piazzas ringed by wine bars, and authentic eateries.

Approximately 40 miles southeast of Antalya, you will find the beautiful coastal resort of Kemer at the foot of the majestic Taurus Mountain. Enjoy a walk along the promenade and a visit a reconstructed tent city that reflects the life of the Turkish nomads. You can watch carpet weavers at work and sample Turkish specialties such as ayran (yogurt drink) and gözleme (pancakes). Close by is a cable car that lifts you right to the top of Tahtali Mountain (2,365 metres).

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.

A ski town that is also an authentic ranching centre, Steamboat Springs is more down home than glitzy. Cowboy hats and ski boots are equally welcome on the city's friendly streets. The place where downhill skiing first flourished in the United States, Steamboat Springs remains a premiere slopes destination. But the town also offers outdoor recreation of every stripe and season. And after a long day hiking, schussing or shopping, you can relax in one of the natural hot springs for which the town was named.

Mombasa, with a population of 900,000, is no sleepy seaside village. Its beachfront hotels appeal to travellers in search of sun, sand and surf, while its Arab, Indian and colonial European heritage makes for a wide variety of sights to see. Can't find a taxi? Travel by tuk-tuk, a three-wheeled auto rickshaw.