This is the Florida that became the first site of European settlement in the New World, the Florida where exotic animal life thrives amid one-of-a-kind landscapes, the Florida that has inspired writers and architects, and the Florida which has a major collection of European art concealed behind its souvenir shops.

You'll feel more like an explorer than a tourist in the 'other Florida', but everything mentioned in this article is within a few hours' drive of Orlando. Venture off the beaten track and you'll find a Florida that you've never dreamed existed – and one that you'll wish you'd found sooner.

If you think Florida's wildlife begins and ends with Donald Duck, you're in for a shock – and the biggest shock for most visitors is the discovery that 30,000 alligators roam at will across the state. Alligators are not the eat anything predators of popular imagination but a vital cog in the state's eco-system – which is why illegal hunting or feeding of them is punishable with a prison sentence and a hefty fine.

Alligators do their most important work in the Everglades, where their powerful tails dig `gator holes' to create the ponds which allow them, and other wildlife, survive the dry winter months. To explore the Everglades, try starting at Flamingo, a small settlement at the southern-most tip. Cabins can be rented for overnight stays and great boat trips are on offer to explore the mangrove swamps and the wildlife that lurks there.

And if you do encounter an alligator in the wild, do not be unduly alarmed. The creatures are wary of humans and will back away if approached – though this is not something that you should be put to the test.

Important though they may be, alligators are not the world's pettiest creatures – a title that might be better applied to Florida's roseatte spoonbills, gorgeous pink-plumed birds, often mistaken for flamingos. Once almost decimated for their feathers, these lovely birds are now widely found in the Everglades and throughout the Florida Keys, a 100-mile chain of islands running south fro Miami and linked by a road from the mainland.

Travel the length of the Keys (a fabulous drive in itself) and you will cross Big Pine Key which, together with the big pine trees that give it its name, is home to a unique species of dwarf deer: each no bigger than a large dog. The deer provided food for sailors and locals for many years but the 400 that remain enjoy legal protection. Delightfully tame creatures, the deer are usually found frolicking in residents' gardens.

Dozens of open-air bars aid the anything-goes atmosphere of Key West, the final stop on the Keys trail and much closer to Cuba than mainland Florida.

Snorkelling, people-spotting, shopping and watching the famously stunning sunsets are the main action in this lively, pretty town. Many American writers have resided in Key west but none of them more famously than Ernest Hemingway, who bought a house here in 1931 and stayed until he moved to Cuba in 1940, storing his manuscripts in a Key West bar called Sloppy Joe's.

The bar still exists, as does Hemingway's plantation-style house, which is now a museum allowing a peek into the writer's living quarters and his deer-head-dominated study.

While Hemingway is a literary heavyweight of international repute, a writer clearer to Floridian hearts is Marjorie Kinnan Rawlings, who ran away from New York and her husband in the 1930s to tend an orange grove in the tiny village of Cross Creek, north of Orlando.

Here, Rawlings wrote the Pulitzer Prize-winning story, The Yearling, and Cross Creek, an Archers-like story of everyday life in the tiny community. She also penned a book of recipes for local delicacies such as catfish, alligator tail and cooter (a soft-shelled turtle). After a visit to Rawling's restored home, drop into the Yearling Restaurant which serves all these dishes.

Further north, St Augustine is the US's oldest site of permanent European settlement. Founded by the Spanish in 1565 and razed by Sir Francis Drake in 1586, the town provided an escape route for British ex-patriots during the American Revolution. Unspoilt by development St Augustine has the size and even the looks of a small Mediterranean town. Along its short streets, carefully restored homes provide a reminder of the power struggles that marked its early years.

It's common knowledge that the space shuttle blasts off from the Kennedy Space Center on Florida's east coast (well worth a visit if a launch is on), but it's less widely known that the shuttle crew's departing view of earth is the Merritt Island National Wildlife Refuge, a broad marshy expanse inhabited by alligators, racoons, armadillos, bobcats and bald eagles.

Also along the east coast, sea turtles give up the security of the ocean for the only time in their lives to steal shyly ashore and lay their eggs under cover of darkness. Book a place on a stealthily guided tour to observe this summer ritual and the prize will be one of natural Florida's most amazing and rewarding sights.

Alongside the turtles' eggs, each tide washes shells of every shape, size and colour onto Florida's beaches. The finest selection are found on Sanibel and Captiva, charming twin islands off the state's west coast with unspoilt beaches, nice restaurants and bars and peaceful walks.

Island businesses give away shell charts to help beachcombers identify their finds and the popularity of shell collecting has led to the bent-over condition known as the 'Sanibel stoop'.

From Captiva, boat trips run to and from neighbouring islands, but the real reason for putting to sea here is to watch dolphins leap from the water and turn unprompted synchronised somersaults to the applause of surprised tourists – a much better way to marvel at the creatures' abilities than seeing them perform tricks in the state's myriad marine-life parks.

St Petersburg is best known for its 25 miles of fine-sanded beaches but the town itself boasts the world's largest collection of paintings by the famed Spanish surrealist Salvador Dali: The collection, acquired by an American friend of the artist, includes over 1,000 pieces, several of which are so large that they occupy a specially deepened section of the gallery. Even if you don't know a thing about Dali when you arrive, join the frequent free guided tours and you'll leave much the wiser.

South of St Petersburg, Sarasota is another town with an unexpected stash of fine art. Millionaire circus owner John Ringling took a shine to Sarasota during the 1920s, making it the winter base of his circus and lavishing $1.5 million on a Venetian-style mansion for himself and his wife.

Next to the sumptuous house, Ringling erected a museum to hold what is now one of the country's greatest collection of Baroque art, including five canvasses by Rubens, which he amassed on shopping expeditions to Europe.

A visit to the Ringling home and museum shows that unlike many American millionaires of his time, Ringling never allowed his spending power to cloud his sense of style. What could have been a vulgar show of wealth is actually a triumph of good taste and proportion – right down to the estate's mock 15th-century Italian palazzo and its imitation classical Greek and Roman statuary.

Cop show Miami Vice helped publicise the Art Deco area of Miami Beach, where scores of perfect 1930s pastel-coloured buildings, decorated by porthole windows and topped by pretend ship funnels or miniature lighthouses, are best appreciated with a guided walking tour.

Alternatively, just hang out at one of the hyper-trendy bars that line the beachfront Ocean Drive, watch the international model shoots and sundry beautiful people and generally just get into the groove. If you're in the mood for a swim, however, and can't face baring your pale torso amid the perfectly bronzed flesh on show here – the beach beside the Art Deco district draws Florida's finest physiques – head across the city to Coral Gables.

Florida has thousands of swimming pools – look out the window as the plane comes in to land and you'll see dozens of them – but none are quite like the Coral Gables' Venetian Pool, where palm-studded footpaths, coral rock caves and Venetian-style bridges are as much an attraction as the water.