Cartagena de Indias is a serendipitous treasure for travelers to South America, a nearly undiscovered city. The old section of the city, behind fortified walls, is a Spanish colonial town that is almost intact. In fact, this city on Colombia's north coast has changed so little since its heyday three centuries ago that it looks like a classic film set.

Colombia is a country of rich, varied terrain: high, cold mountains (the climate in Bogota', the capital, resembles England's); fertile, terraced coffee-growing lands; impenetrable jungles teeming with wildlife; austere pre-Colombian sites; broad rivers. It is the only country in South America with vast coastlines along both the Pacific and the Caribbean, and it is here, on the Caribbean coast, that you find Cartagena, a mere 4 1/2 hours flying time from New York, two hours from Miami.

Cartagena is a magical mix of Spanish colonial architecture and Caribbean laissez faire. The climate is tropical, the tempo laid-back. There are bougainvillea and flame trees and palms, bananas growing outside the hotel window and parrots squawking in the lush gardens. The population of half a million is friendly, and many of the people are extraordinarily beautiful -- with golden complexions and green eyes.

Cartagena is really two cities: the old colonial town that is its heart, and the modern provincial capital that has grown up around it. The original walled city resembles a knee surrounded by water: the Caribbean on the west, the Bay of Cartagena on the south, lakes and lagoons on the north and east. Stretching south from the knee, like a boot with the foot turned in, is a long spit of land known as Boca Grande, which offers the Caribbean and beaches on one side and the bay on the other. At the heel of the boot is El Laguito, the best of the city's resort areas.

A decade or so ago, there was an attempt to turn Cartagena into a major resort town for foreigners (Colombians have always come here for holidays). New hotels were built, others refurbished. Then the dollar fell. Americans stayed home and the project faltered. And Cartagena was left almost as before, barely discovered, at least in comparison with other Caribbean cities.

The proximity of good beaches to the old city makes Cartagena special, and the old town itself is a dream. It is so larded with otherworldly charm -- the secret courtyards blooming with exotic flowers, the arcaded streets -- that you almost expect Errol Flynn to leap from the rigging of some frigate in port by the light of candles sputtering in a wrought-iron candelabra.

Cartagena has always been the stuff of legends, from its founding in 1533 by Pedro de Heredia -- often referred to as the noseless Spanish conquistador. After putting down the local Kalamari Indians, de Heredia established Cartagena. Treasure wrested from the natives, it is said, included a porcupine made of gold that weighed 138 pounds and was later melted into bullion. The story of Cartagena is the story of the Spanish imperial plunder of South America, of the great pre-Colombian cultures and the rich, natural resources.

Walls and fortifications were built to protect the city almost from the beginning. But in spite of these, in 1586 Sir Francis Drake (referred to in local literature as "the notorious English brigand") sacked the city and held it for ransom. King Felipe of Spain subsequently increased the fortifications to spectacular dimensions.

There were originally two approaches to Cartagena from the sea, one at Boca Grande (Big Mouth), the other at Boca Chica (Little Mouth). After an attack on the city in 1741, Boca Grande was blocked off, leaving Boca Chica as the only route in. To the north of Boca Chica is the island of Tierra Bomba, and at its tip the fortress of San Fernando, which is an hour by boat from the city. The fortress, one of the most impressive ever built on the continent, has intriguing vaults and a sinister moat. Condemned prisoners were put to death in that moat, which was filled with sharks. Begun in 1753, it took 30 years to finish.

After Colombia's liberation from Spain in 1821 by Simo'n Boli'var, Cartagena's importance decreased. It became a sleepy backwater, and although there were occasional attempts at modernization, most -- except for a few ugly 1930s buildings -- were, happily, thwarted.

Cartagena's main tourist season is between December and April, when hotel prices soar. The best hotel is the Cartagena Hilton at El Laguito, a pleasant high-rise where all the rooms face the pool and the beach beyond. There are thatched cabanas, tennis courts, a bar (which would be a lot more appealing without the hideously loud and bad music), a coffee shop where the sandwiches have names like El Drake, and a really good restaurant, El Tinajara de Dona Rosa. The service is friendly and efficient; this is a good hotel that works.

But it is the old city you come for, a mile or two from the beach by taxi or, at night, horse-drawn buggy. As you pass through the city walls on weekends or at night, when there is almost no traffic, there is a sense you have fallen through a silver screen into another era.

Laid out on a traditional Roman grid scheme, Cartagena's streets are lined with houses that clearly reflect their colonial tradition. This is domestic architecture by way of southern Spain. The Moorish influence is everywhere -- in the archways, the filigreed balconies, the tiled courtyards. Peculiar to the houses here are the ground-floor bay windows called panza (belly). These served as window seats, where strictly chaperoned young women could sit chastely behind wooden grilles and flirt with their lovers, who stood outside.

The largest square in Cartagena and a good starting place for a walking tour of the old city is the Plaza de la Aduana, which has a statue of Christopher Columbus in the middle. Noteworthy buildings on the square include the old Customs House -- which is now the city hall -- the art gallery of the Banco Ganadero and several splendid old colonial mansions. Around the corner from the square are the church and monastery of San Pedro Claver, built by the Jesuits in 1603. It is dedicated to Claver, a Spanish nobleman who spent his life caring for the black slaves brought from Africa to work on the city's fortifications.

Several blocks away, past cafe's and artisans' shops, is the Plaza Boli'var. This is one of the prettiest squares in the city, with a statue of the revolutionary leader in the center. On one side is the Palace of the Inquisition, which was founded early in the 17th century and rebuilt in the 18th. It is the best example of colonial baroque architecture in Cartagena. Behind its gates, the leafy courtyard gives lie to the sign over one door that reads "chamber of torture." There is also a legend inscribed on the garden wall recounting the horrors of the local inquisition. The building now houses a museum, which includes fine examples of pre-Colombian art.

If you leave the Palace of the Inquisition and turn left on the Calle Santo Domingo, in a few minutes you come to the lovely church of Santo Domingo. The oldest in Cartagena -- it was built in the 1570s -- the church contains a famous wooden Christ; legend has it that if anyone tries to remove the Christ from the church, it will grow too large to be taken through the door. The church is on Santo Domingo Square, where there are cafe's and taverns that draw young people at night.

Many private houses in Cartagena have recently been restored, and several are open to the public. One of the grandest of these colonial mansions is the house of the marquis de Valdehoyos, a rich colonial flour and slave trader, on the Calle de la Factoria. Some of the scenes from "The Mission," a film about the Jesuits in 18th-century South America starring Jeremy Irons and Robert DeNiro, were shot in the house, which has marvelous balconies and courtyards. The film, which will be released in the fall of 1986, was shot on location in Cartagena and makes the most of the local architecture.

Another private mansion houses the Queimada Tavern. If this looks a lot like an English pub, that's because it was the setting for another movie, the 1968 slave-revolt drama "Queimada" or "Burn!," starring Marlon Brando.

There is also the Bodegon de la Candelaria on the Calle de las Damas, which has not only been restored to its colonial splendor but serves at night as a romantic candlelit restaurant. It was at the Bodegon that Our Lady of the Candelaria, the patron saint of Cartagena, is said to have appeared to Father Alonso de la Cruz, giving him instructions for the building of the church and monastery of Santa Cruz on La Popa hill outside town.

Before taking a taxi to La Popa for a panoramic view of Cartagena, leave some time to simply wander the city streets. There are interesting architectural details everywhere, and streets so narrow you can simultaneously touch the walls on both sides.

A short taxi ride from the city will take you to the monastery of Santa Cruz, founded in 1608. To build La Popa, as it is commonly known, Father de la Cruz destroyed the temple the Indians had built for their idol, Burizago, a golden goat, which he threw down what is now known as the Goat's Precipe (Salto del Cabron).

Another panoramic view of Cartagena is from the best restaurant in town, the Club de Pesca. Located in a restored 17th-century fort, San Sebastian del Pastelillo, it sits at the tip of Manga Island on the edge of the bay.

You dine on the ramparts of the old fort shaded by ancient banyan trees. As the sun goes down and Cartagena's lights come up, you watch the gliding boats and the alluring city. The scene is so pleasant you may wonder if it is a film set or merely the real thing. In the end, it doesn't matter: In Cartagena, illusion and reality are both part of the same magic.