It took scant minutes after arriving on Martha’s Vineyard to get a fix on what the island is all about.

I passed winding driveways leading to mansion-size homes with gentle names like Swans Way and Sweet William Path. Rickety roadside tables were laden with flowers, eggs and vegetables for sale, and handwritten signs indicating how much money to leave for purchases made on the honor system.

Martha’s Vineyard, an island off Cape Cod in Massachusetts, is best-known as a tony hideaway for celebrities, politicians, and the rich and powerful. That reputation was enhanced last summer when President Obama and his family took their first vacation there since moving into the White House.

They were the latest in a varied list of celebrities who have visited, and in some cases built homes, there. Nathaniel Hawthorne and Daniel Webster dropped by in the mid-19th century. Barack Obama joined Ulysses S. Grant and Bill Clinton among sitting presidents who have spent time. If visitors think they spotted Ted Danson and Mary Steenburgen, James Taylor or Carly Simon, they’re probably right.

They are among folks who discovered the appeals of the triangular island — nine miles wide by 23 miles long. As one resident claimed, it’s “big enough to hide out on and small enough to do just about everything you want in a few days.”

My wife Fyllis and I agree with that observation. Our plan was to delve into the island’s history, sample the full menu of activities, and learn what makes it so special to luminaries. We weren’t disappointed on any score.

The history of Martha’s Vineyard encompasses the Wampanoag Native Americans, immigrants from England, African-Americans and an influx of people from Portugal. A small Wampanoag reservation serves as reminder that some 400,000 members of that tribe inhabited nearly 70 villages throughout New England in the 1600s. They were there as a parade of explorers began to arrive, and when the first English settlements were established in the mid-17th century.

It wasn’t long before slavery came to the island, to provide workers on sheep farms that produced wool and woolen cloth for export, and on whaling ships. After slavery was abolished in 1783, a small neighborhood of free African-Americans sprung up in what now is the town of Oak Bluffs.

Rather than the simple shingled houses built by early settlers, homes in Oak Bluffs show a different face. They are whimsical wooden cottages adorned by turrets and towers, ornately trimmed gables and porches, all painted a variety of pastel shades. That enclave became and remains a vacation destination for African-American doctors, lawyers and other professionals from major East Coast cities.

Each of the other towns on Martha’s Vineyard also has its own distinct character. Vineyard Haven was one of New England’s busiest ports during the time of wind-powered ships and whaling. Today it’s home to the largest year-round population on the island, about 2,000 people. Its historic neighborhood contains a number of 19th-century houses.

Wandering in Edgartown is akin to a stroll through an early 19th-century seaport. Brick sidewalks along narrow tree-shaded streets lead past stately Greek Revival homes that were built by whaling captains. Clinging to its nautical past, Edgartown is a popular yachting center with a protected harbor.

The other tiny towns are located at the rural, western end of the island. There, stone fences enclose gently rolling fields where sheep graze, oblivious of spectacular views of the Atlantic Ocean in the distance.

West Tisbury is little more than an intersection overlooked by a church, town hall and general store. The largest homes once were owned by sea captains and some are occupied by their descendants. Alley’s General Store, in business since 1858, is a gathering place for locals and visitors alike.

The 963 residents (by latest census count) of Chilmark live among low hills with views of the sea. For visitors, it serves primarily as a landmark for two other destinations.

Menemsha is less a town than a working harbor. Weather-beaten boats chug out to sea and return with catches of fish and lobster, which modest restaurants and carryout shops prepare. Many locals rate Larson’s as the best place to order clam chowder and lobster rolls, and The Bite for fried clams.

Aquinnah, on the eastern tip of the island, is known for a mile-long stretch of multi-colored cliffs overlooking the beach. Nature has fashioned layers of sand, clay and gravel into a kaleidoscopic mixture of reds, whites and grays.

Those seeking an even more isolated setting may hop aboard the minuscule “On Time” ferry for the one-minute ride to Chappaquiddick. That tiny dot in Edgartown Harbor became an island in 2007, when a storm breached the land connection.

Seclusion is what residents of “Chappy” seek, and seclusion is what they enjoy. For visitors, attractions include a seven-mile-long beach, one paved road and a number of sand tracks for hiking and biking. Plovers, terns and other birds make their home in the salt marsh. Most day-trippers also explore Mytoi, a 14-acre Japanese garden with meandering paths, fish-filled ponds, a graceful arched bridge and varied plantings.

Along with an inviting beach on Chappaquiddick, Martha’s Vineyard has more than a dozen stretches of sand that tempt warm-weather visitors. Three-mile-long South Beach near Edgartown is most popular, and most crowded, during summer months, especially by people who like wave action. Those seeking more gentle surf prefer the Oak Bluffs, Menemsha or Joseph Sylvia beaches.

The list of other to-do’s extends to outstanding fishing for blues, striped bass (rock fish), bonita and other scrappy fighters; spotting some of more than 300 species of land and water birds that inhabit and visit the island, and pedaling on 44 miles of flat bike paths and roadways.

As hikers, Fyllis and I had a wide choice of trails. We opted for the Manuel F. Correllus State Forest, a 5,100-acre tract of grasslands, woods and meadows crisscrossed by eight miles of flat hiking tracks.

Whether experiencing the pleasures of an inviting beach, reliving an intriguing chapter of American history, or simply hanging out at a place where numerous celebrities head for a bit of rest and relaxation, Martha’s Vineyard has variety enough to fill many a traveler’s wish list.

Victor Block is a freelance writer who lives in Washington, D.C., and spends summers in Rangeley.