Getting from Northeast Florida to that impossibly blue stretch of the Aegean requires a bit of strategy, since there's no realistic nonstop routing to speak of — business class from Jacksonville to Mykonos always involves at least one connection, and typically two, given that Mykonos's small airport handles seasonal regional traffic rather than widebody long-haul flights. The most sensible itineraries funnel through a major European gateway before dropping down to a narrowbody hop into JMK. British Airways offers a strong option via London Heathrow, where their Club Suite — with its direct-aisle access and sliding door on the 777 and A350 fleets — makes the transatlantic leg genuinely restful before a same-day or next-morning connection south. Lufthansa routes through Frankfurt or Munich, and their Allegris business class, now rolling out on select 787 and A350 routes, is worth seeking specifically if your itinerary allows for it, since older long-haul configurations still lack the same privacy.
Aegean Airlines becomes essential for the final leg, operating from Athens into Mykonos on a short regional hop that, while not a widebody business product, is a comfortable and quick way to finish the journey after a long transatlantic flight. My preference, built from flying this corridor repeatedly, is to route through Frankfurt or Munich on Lufthansa rather than London, since Athens connections from German hubs tend to have more forgiving layover windows and Athens International itself is a far calmer airport to transit than Heathrow during peak Mediterranean season. If you land in Athens with several hours to spare, it's worth booking a day pass to a lounge in the Athens terminal rather than rushing straight to the Aegean gate — the domestic-to-island departure area gets crowded fast in July and August.
April, May, September, and October remain the sweet spot for this route, both for pricing and for avoiding the peak ferry-crowd chaos that descends on Mykonos in midsummer. Shoulder-season business class fares from Jacksonville can fluctuate significantly week to week depending on carrier promotions across the Atlantic, so setting up fare alerts for this specific JAX–JMK routing is the smartest way to catch a premium seat without overpaying.