One of Islam’s most holy cities, Medina, is a sprawl of minarets and shops wrapped around the landmark, the Prophet’s Mosque. Like the rest of central Medina, it’s for Muslims only and is surrounded by plenty of hotels and eateries to welcome the pilgrimage crowd.

The legendary Hamptons, a cluster of wealthy enclaves on Long Island's South Fork, remains a celebrity summer playground, with splashy restaurants and nightclubs galore. But lovely beaches, fishing and kayaking attract off-the-A-list visitors, as well. Old money oozes throughout Southampton, while new wealth reigns in East Hampton. Montauk is a hit with fishermen and surfers. The Long Island Railroad travels the Hamptons in an hour. The Sag Harbor Whaling Museum and Montauk lighthouse are popular stops.

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.

The Zanzibar Archipelago, located in the Indian Ocean 15 miles off the coast of Tanzania, is a breathtaking spot to escape from the world. You’ll enjoy clear, turquoise-blue water; shallow sandbars perfect for wading; and many small, nearly deserted islands virtually unvisited by tourists. Explore the World Heritage Site of Stone Town, Zanzibar City’s old quarter. Or just go beach to beach between tiny fishing villages—each one's better than the next.

Pretoria is a vision of purple, thanks to its plethora of blossoming trees that gave the South African metropolis its nickname: Jacaranda City. Give in to the animal magnetism of the National Zoological Gardens of South Africa, then get up close and personal with the big, bad kitties of the Cheetah Research and Breeding Centre. The buildings of Pretoria reflect diverse architectural styles and influences, creating a unique urban landscape.