If you're looking for that someplace where it's always five o'clock it's entirely possible that the paradise you seek is Key West, aka the Conch Republic aka Margaritaville (in the best Jimmy Buffet style). Key West also happens to be the southernmost point in the Continental United States, but that's not what has historically brought in a steady stream of artist-types and notable characters (think Tennesse Williams, Ernest Hemingway, former President Truman and so forth). Only four miles long and two miles wide, this out-of-the-way island is blessed with balmy weather, lots of sunshine and surrounded by the only barrier reef in North America which equates to good snorkeling and scuba diving with easy reach, as well postcard-worthy opportunities for underwater photographers (and the sorts of schools that keep anglers well occupied).
While bars and beach rank at the top of the list in terms of "attractions", there's also a surprisingly good assortment of cultural sights to catch in town between drinks, most of them in Old Town, which sprawls out either side of the main drag, Duval Street. On a fairly modest walking tour it's possible to soak up the general trends in typical Key West architecture, enjoy a stop at the Wreckers Museum, explore the former residence of Francis Watlington, a wreck captain (Wreckers Museum), and take in the Mel Fisher Maritime Museum. There's also a Heritage House Museum, a history-oriented museum (East Martello Museum and Gallery) housed in a tower, a Lighthouse Museum and the island's best-known attraction, the Hemingway Home (former home of the novelist, Ernest Hemingway). To really get a feel for what makes Key West tick, ditch your snorkelling gear come sunset and head for Mallory Square, where the people-watching and the sunsets both count as reliable entertainment.
When the weather is fine though - which is every day really - the place to be is out on the water. Some of the best snorkelling and diving is to be found offshore, but even for those in town short a water craft it's easy enough to join one of the many organized excursions that regularly boat around to the most popular sites. Key West doesn't have the best beaches in the island chain but it does have three decent public strips of sand and one off Fort Zachary Taylor for a small fee. When you're ready for a change of scenery, consider booking passage out to one of America's little-known national parks, Dry Tortugas, which can be seen as a day-trip or enjoyed for a longer stretch courtesy of Garden Key campsites.
Key West is about 160 miles from Miami at the endpoint of US-1.