Madeira has over 90 miles of coastline, but it doesn't have a beach. A day of lazing around on the sands involves a two and a half hour catamaran trip (schedules available at www.portosantoline.pt) or a 20-minute flight (schedules available at www.anam.pt) to the neighboring island of Porto Santo. Either option is worth it, thanks to one of Europe's best beaches—five miles of almost untouched sand —and a house where Columbus once lived.

Captain Peter Bristow will assist your search of giant blue marlin aboard the Katherine B for about $1,200 per day for the whole boat—round up half a dozen people, and the trip can be a bargain (291 752 685 or 917 599 990; www.fishmadeira.com; bristow@netmadeira.com).

The breezy hilltop suburb of Monte includes a church where Charles I, last of the Hapsburg emperors, is buried. But the real attraction are rides on the world-famous carro de cesto street toboggans. A pair of white-suited, skilled drivers will push and steer your wicker sled through the streets and down three miles of steep, winding roads back to Funchal. The cost is about $12; contact Carreiros do Monte, Sitio da Igreja (291 783 919).

A full-scale mahogany replica of Columbus' ship, the Santa Maria sails on Wednesday and Sunday evenings at 7:15 p.m. from Funchal harbor. The 90-minute trip takes you around the coast of Madeira. Contact Marina do Funchal (291/220-327 or 291/225-695).

The tourist office in Funchal lists levada walks on narrow paths alongside the narrow irrigation canals that flow horizontally around the island's hills. Particularly scenic are those from the village of Ribeiro Frio. Most can be reached by bus.