Nassau's Straw Market: you can buy bags, mats, hats . . .

In their rush to get to the Out Islands, to those lyrically named places like Eleuthera, Bimini, and Abaco, visitors to the Bahamas are passing up a good bet in New Providence Island and its pulsing capital, Nassau.

As I poked about the old town one sultry morning, it occurred to me that if Nassau had nothing more to offer than its buzzing new Straw Market on Bay Street , it would be worth the stop. Indeed, if you dodge the traffic and ignore the heat, other surprises lie hidden away on the back lanes, down at the quays, and up in the palmy heights of the Big Conch.

What makes Nassau all the more appealing is the knowledge that the sand and surf, the tennis and golf of Cable Beach, are only a few miles away, while across the soaring little bridge to Paradise Island wait even more diversions, not the least among them a hot white beach that measures up to any in the chain.

Rawson Square in the heart of Nassau seemed the logical spot to launch my urban exploration one morning at 9. Three green-shuttered Georgian mansions, which have served as houses of government for centuries, stand at the edge of the square. At the center sits a stony white Queen Victoria, flanked on the lawn by two yellow-wheeled cannons. On the ground floor of one of the government buildings is a tourist information center where fresh maps and brochures are laid out each morning and guided walking tours of Nassau begin.

With the right materials and enough leg power, I was to find, Nassau can be nicely done on one's own. And just when you hit a snag, there is a member of the Royal Bahamian Police, done up in white jacket, pith helmet, and dark trousers with wide red stripes, ready to spell out careful directions.

Rawson Square gives onto the harbor, where a battered lineup of boats bound for the Out Islands was taking on passengers and cargo, everything from bags of cement to cases of soft drinks. I walked along the throbbing, tooting quays until I came to the back side of the Straw Market, just beginning to throb itself. Bahamians will remind you proudly that until the government built a permanent marketplace, Nassau's straw weavers made do with a ragtag hangout around Rawson Square.

By 8 or 8:30 every morning the women are laying out their baskets, bags, hats , mats, wastebaskets, and flower-pot holders in the two-story arcaded concrete structure which covers an entire city block. Also for sale are paintings, conch shells, T-shirts (inevitably labeled ''It's Better in the Bahamas''), necklaces, and wood carvings of birds and animals and human faces done in wild tamarron and mahogany. For an island market, the sell is surprisingly soft. ''Can I help you, darlin'? Can I sell you something?'' are the gentle pleas that follow you from stall to stall.

Just a few blocks above the Straw Market and the duty-free shops of Bay Street, I left behind the clamor of a weekday morning and found myself staring into the muzzle of an old cannon. I was at the foot of a steep stairway leading to the pink and pillared Government House. Halfway up the steps stands a carefree Christopher Columbus, leaning on his sword. At the top, almost as still as the statue of Columbus (who came ashore here in 1492), a helmeted sentry with musket and unsheathed bayonet stood watch at the doors of the Government House, home of the governor general, Gerald Cash.

You can't get past the guard and into the Cash residence, but his office next door is open to the public. There in the reception area a large, burnished wood board lists past governors and the English kings and queens they represented, going back to 1670. One name stands out like neon - the Duke of Windsor, who served the Bahamas from 1940 to 1945 - and, despite world events, helped to establish Nassau as a fashionable international resort.

Up in these well-shaded heights, surrounded by stone walls and iron gates, are assorted historic houses in various stages of repair, from shipshape to shabby. One that stands tall, just across the road from the Government House, is Greycliff, a 12-room Georgian inn and restaurant with a breezy, lived-in feeling. Nearby, another handsome shuttered Georgian house, the Buena Vista, has six guest rooms and a popular restaurant, which spreads across a broad, shaded terrace in back.

Not much produce is raised on the sandy coral acres of the Bahamas, but what there is shows up daily at a fruit, vegetable, and fish market scattered beneath the bridge to Paradise Island. Under striped umbrellas are piles of okra, tiny limes, bananas, corn, red and green peppers, yams, and bags of pigeon peas - little brown pellets the islanders incorporate into their beloved pea and rice dishes.

Small boats nudged up to the quays with their fresh loads of fish and conch. Men bent to the task, hammering holes in the conch shells, then inserting a knife to remove the meat, which would become the stuff of stews and soups. Suddenly in this thicket of motley craft appeared a shiny speedboat. Its well-heeled young passengers looked straight from Cap d'Antibes or Sardinia. ''We want a watermelon,'' one of them shouted, and somehow from the mounds of produce their quarry was uncovered. Then they were gone, on a long funnel of surf, and life on the docks in old Nassau returned to normal.