10-Nights Royal River Luxury Hotel: Idyllic Retreats Collection from $5,479

Tenerife is the largest of the Canary Islands, and offers much to see and do. It has both flat areas (covered with banana plantations) and mountainous areas. Its mountainous terrain provides plenty of recreational opportunities, and beautiful architecture and landscapes abound.

The volcanic Mount Teide, the centerpiece of Teide National Park, is the highest mountain on Spanish territory. More than 12,000 ft/3,720 m tall, it soars above much of the island. Take a tour or drive to the summit and then switch to a cable car for the final ascent.

The northern side of the island is green and tropical, and the southern side is dry, with near-desert conditions. Tenerife's largest city is Santa Cruz de Tenerife, where there is a wide variety of tourist accommodations and activities—including one of the best Carnival celebrations in Spain (on par with the one in Cadiz). It also has some nice colonial buildings and pleasant parks—a good choice as a base if you prefer to stay outside the typical tourist resorts.

North of Santa Cruz, occupying the northeastern part of the island, is the green and rugged Anaga mountain range, a good spot for organized hikes. On the western coast is Puerto de la Cruz, a resort area that attracts a lot of visitors.

The south, which has the island's best beaches, is geared to huge crowds with full-service resorts and apartments in the concrete jungles of Los Cristianos and Playa de las Americas. At Guimar, near the midway point up the eastern coast, there are stone pyramid platforms, believed by Norwegian ethnographer Thor Heyerdahl to prove ancient links with the Americas. They are preserved in the Parque Etnografico Piramides de Guimar.