Low-key Legian is the picture of relaxation. Just about the only action the beach gets is from the evening fire spinners, whose quick hands pass orange balls of light through the sky. Surfers, body boarders and sunbathers share the calm sands happily. There are plenty of markets, cafes and restaurants to satisfy your cravings for merchandise and meals. If you itch to mingle with locals, you might be able to join in the game of football that happens nightly on Blue Ocean Beach.

You can eat very well—and very cheaply—in Taipei. The restaurants may not look posh, but the quality of the food is superlative. And there’s a huge variety of restaurants—in addition to local Taiwanese specialties, you’ll find regional cuisines from all over China, as well as great Indian, Japanese and even Italian options. Just make sure to leave some room for snacks—street-vendor food here is addictive.

Home to nearly nine million and powering an economy that exceeds both Hong Kong's and Thailand's, Osaka packs quite a punch. The confident, stylish city is a shopping hub, with fabulous restaurants and nightlife. It's an ideal base for exploring the Kansai region: Kyoto's World Heritage Sites, Nara's temple and Koya-san's eerie graves are within 90 minutes by train. Top city attractions include the aquarium, Osaka Castle, Universal Studios Japan and the futuristic Floating Garden Observatory.

Sometimes referred to as the capital of Africa, Addis Ababa is a buzzing hub of economic, social and political activity and home to such notable offices as the African Union and the United Nations Economic Commission for Africa. The diversity of its people is reflected in the many churches, mosques and museums, including the Ethiopian National Museum which houses the fossilized skeleton of Dinkinesh, or Lucy, the Australopithecine discovered in the area in the 1970s.