Ever since the oil tycoon Henry Flagler turned the alligator-infested jungle known as Lake Worth into a tropical paradise for the 1 percent (it was the Gilded Age, after all) with palatial hotels and a railroad to serve them, Palm Beach has been synonymous with the biggest and the best: fortunes, jewels, scandals. The 16-mile-long island of extravagant mansions, tony retailers and fanciful landscaping is rich in history and significant landmarks, from the magnificent Mar-a-Lago estate (completed in 1927 for Marjorie Merriweather Post, now Donald Trump’s private club) and the Paramount Theater (a former movie palace that houses a trove of vintage screen star photos) to St. Edward’s church (where the Kennedys worshiped) and Green’s Pharmacy (where John F. Kennedy enjoyed burgers in the luncheonette).But Palm Beach is also a small gem offering simple pleasures. You can ride a bike anywhere or linger over coffee at a lunch counter and never be more than a block or two from the beach. Even the new Orange Line trolley that shuttles riders between arts destinations in Palm Beach and neighboring West Palm Beach adds a down-to-earth touch to this high-rolling town (and it’s free!).