Palm Beach is a city in Florida.
Palm Beach International Airport (IATA: PBI), 1000 Turnage Boulevard, (561) 471-7420, . This is a small, yet highly adequate airport. While both the Miami and the Fort Lauderdale airports are busy, PBI is easy to get in and out of, and is about 2 min from downtown West Palm Beach. Travelers flying into South Florida or the Bahamas should strongly consider PBI.
Greyhound has a bus station in Downtown WBP, right next to the Tri-Rail station. 
To get from the airport to Palm Beach by transit, you can take the #44 to the Tri-Rail station, and then take the #41 bus.
TriRail has stops at the West Palm Beach Airport towards Magnolia Park and Miami Airport.
The #41 bus is the only form of transit on the island, but unfortunately, it only has a few trips a day, and doesn't run Sundays.
There are many beaches that are clean and open for swimming.