Kids jump off the American Legion Memorial Bridge, better known as the ‘Jaws’ bridge for its role in the movie, which was filmed on Martha’s Vineyard.

Once upon a time, Martha’s Vineyard was a place of fishing villages and farms. Then came the summer people, eager to escape broiling Northeastern cities, along with counterculture types looking to break away from mainland mainstream conventions.

In 1975, a certain animatronic shark arrived, and the still relatively sleepy Martha’s Vineyard cemented its spot in American culture as the filming location for Steven Spielberg’s “Jaws.”

Its profile now dramatically raised, the island entered a new era when Bill and Hillary Clinton spent two weeks there in 1993. Other big names followed. Today, Vineyard mainstays include Larry David and Spike Lee, as well as Barack and Michelle Obama. As the wealthy elite staked their claim, prices for everything—from lobster rolls to seaside shacks—skyrocketed.

I wondered: Beyond the preppy Vineyard Vines clothing stores and gleaming Escalades, does the island still offer space for quiet contemplation and artistic inspiration? Can you enjoy it without a trust fund?

“That still, to a surprising degree, exists if you know where to look for it,” said A. Bowdoin Van Riper, a research librarian at the Martha’s Vineyard Museum. On a recent trip, I resolved to find it.

I experienced sticker shock immediately, while looking for a place to stay. During peak season, the population can swell to 100,000, five times the number of full-time residents. The rare hotels demand sky-high prices, say, $1,500 for a two-night, late-August stay at the Harbor View Hotel near Lighthouse Beach. A gingerbread-like cottage in Oak Bluffs I found on Airbnb momentarily excited me—until I saw the price, $1,309 for two nights.

Finally, I came across Martha’s Vineyard Family Campground, a welcoming, sprawling complex about 4 miles north of the airport in West Tisbury.

Martha’s Vineyard Family Campground is one of the few affordable accommodation options on the island during the summer high season.

While most people arrive by ferry, I had some frequent-flier miles to burn, so I flew direct from Washington, D.C. That left me carless, which turned out just fine.

From the airport, near the southern edge of the Manuel F. Correllus State Forest, I hiked north through unchallenging terrain—an easy trek even if camping gear weighed down my backpack.

The Manuel F. Corellus State Forest is near the airport and home to miles of trails.

During the summer peak season, you can rent two-room cabins for $229 a night at the clean, well-run campground, more than 50 years old. But I paid roughly a third of that to pitch my tent in a remote section. It granted me the quiet solitude I craved, though I still had full-bar phone service and could get essentials (ice cream, gummy bears, seltzer) at the camp store a 2-minute walk away.

I could have rented a car, but further to my quest for frugal simplicity, I made my way to All Star Bike Rentals in Vineyard Haven, where $120 got me a well-maintained, sturdy bike for my whole trip. You can easily navigate the island’s eastern end without ever getting in a car, thanks to bike paths, including a 7-mile route between Edgartown and Vineyard Haven, and a 6-miler from Oak Bluffs to Edgartown.

When I ventured farther, I relied on the island’s surprisingly efficient buses, free through late September. Buses travel just about anywhere you’d want to go, including more remote “up-island” (that’s Vineyard for “western”) destinations like the frozen-in-time fishing village of Menemsha.

Before my trip, the historian Van Riper had stressed the need to get up-island. “Get out of the downtowns of Edgartown, Oak Bluffs and Vineyard Haven,” he advised. He directed me to up-island towns like West Tisbury and Chilmark, explaining that they evoke “the Vineyard as I remember it from my years as a summer kid in the late ’60s.”

I spent a lot of time exploring the island’s western reaches. My most memorable dinner? Not an overpriced, underseasoned fish filet served at a dimly lit table I had to book months in advance. Instead, it was the salmon bánh mì I enjoyed slowly on the porch of the Chilmark General Store among locals who’d gathered to chat, eat or read. Lingering on the porch is not just allowed, but encouraged. “I don’t think I’ve ever been concerned about how long someone would stay on the porch,” the store’s co-owner Joel Glickman said.

The Gay Head Lighthouse, on Martha’s Vineyard’s westernmost point in Aquinnah.

The internet yields countless lists that detail how much celebrities paid for their Vineyard mansions. I started keeping a far more enticing tally of the Vineyard’s offerings: 16 miles of public beach; about 40 square miles of permanently protected forest and wetland; 15 ponds; 40 miles of down-island bike trails. All of it, completely gratis.

“It’s hard to figure out what people are really here for,” said Juli Vanderhoop, the owner of Orange Peel Bakery and an elder in the Wampanoag Tribe of Gay Head, the original residents of Aquinnah on the island’s western edge. “This was a place that could actually give someone respite.”

Good news: It still can.