Palm Beach International Airport: The sensible airport: it is in West Palm Beach, about 10–15 minutes by taxi/rideshare from Palm Beach island depending on bridge traffic; expect roughly $15–25 before tip. Palm Tran Route 44 links the airport area with downtown/West Palm Beach station for a low local-bus fare, but it is slow and leaves you on the wrong side of the Intracoastal for most Palm Beach hotels—use it only if you are staying in West Palm Beach.
West Palm Beach station (Brightline, Tri-Rail and Amtrak): This is the regional rail hub, with frequent Brightline service from Miami and Fort Lauderdale and Tri-Rail from Miami Airport via Fort Lauderdale. For Palm Beach island, take a short taxi/rideshare—about 10–15 minutes and roughly $10–20—or walk only if your destination is at the very northern end of the island; the bridges and Florida heat make it a poor luggage transfer.
Fort Lauderdale–Hollywood International Airport: Useful if fares are much better. Take a taxi/rideshare to Brightline’s Fort Lauderdale station, then Brightline to West Palm Beach; allow about 1½–2 hours airport-to-Palm Beach once transfers and waits are included, plus roughly $25–50 total depending on train fare and ride-hail pricing. A direct car is usually 1–1½ hours, but can be far longer in South Florida traffic.
Miami International Airport: Only choose MIA for a notably better flight. Tri-Rail connects Miami Airport with West Palm Beach cheaply but takes roughly 2–2½ hours to the West Palm Beach station; Brightline is faster once you get to MiamiCentral but adds an airport transfer. Door to door, budget 2–3 hours. A car can take 1½–2½+ hours depending on traffic.