Getting to the Cyclades in comfort requires strategy, since no carrier flies nonstop between the Pacific Northwest and the Aegean. There is no business class from Seattle to Mykonos on a single ticket without a connection, but that's precisely what makes route selection so rewarding for those who know the options: Lufthansa, British Airways, and Aegean Airlines each offer viable paths, typically routing through Frankfurt, London Heathrow, or Athens. Mykonos itself only receives seasonal service (roughly April through October), so your international carrier gets you to a European hub, and Aegean Airlines finishes the job with a short intra-European hop, often in a well-appointed business cabin with blocked middle seats on the A320 family.
My preferred routing has long been Lufthansa via Frankfurt, where their Allegris business class—now rolling out on select long-haul aircraft—offers sliding doors and genuine privacy that outclasses older staggered configurations. British Airways via Heathrow is the other strong contender, especially now that Club Suite has fully replaced the old Club World seat on most 777 and A350 aircraft serving Seattle; the direct-aisle-access design is a meaningful upgrade worth seeking out when booking. One insider tip few travelers exploit: Aegean's short Athens-to-Mykonos business class segment is inexpensive to add and dramatically improves the arrival experience, since Mykonos's small airport gets chaotic during peak summer weekends—arriving on Aegean's business fare grants priority baggage handling that can save twenty minutes on a hot tarmac.
Seasonality matters enormously here. Shoulder months—April, May, September, and October—not only bring better fares but a more relaxed Mykonos, with warm seas and none of the July-August crush. Given the multi-carrier connections involved, fares on this corridor fluctuate more than most transatlantic routes, so setting up automated fare alerts is the smartest way to catch a Lufthansa Allegris or BA Club Suite award or premium cash fare before it disappears.