Mykonos remains stubbornly unreachable by direct service from California, which means the real work of booking business class from San Francisco to Mykonos happens in the connection you choose. There is no nonstop option: every itinerary funnels through a European or Aegean hub, with Lufthansa via Frankfurt or Munich, British Airways via London Heathrow, and Aegean Airlines via Athens representing the three practical routings. Total journey time runs roughly 14 hours in the air, though with connections you should budget closer to 16-18 hours door to door. The factual bottom line: Aegean's Athens connection is the only routing that keeps you on Greek carriers for the entire Europe-to-island leg, landing you at Mykonos's compact JMK airport with minimal fuss.
Each carrier has its own personality in the front cabin. Lufthansa's long-haul segment from SFO increasingly features the new Allegris business seats on select 787 and A350 rotations, with proper closing doors on many configurations — worth checking your specific aircraft before booking, since older 747-8 or A340 business seating still flies some frequencies. British Airways routes you through Heathrow in the Club Suite, its fully enclosed pod with a sliding door that's become one of the more consistent hard products in the transatlantic space; Terminal 5's dedicated Concorde Room lounge makes a long layover genuinely enjoyable rather than a chore. Aegean, while not a long-haul carrier, deserves attention for the final hop — book the SFO-Athens segment in business on a partner, then let Aegean's short Athens-Mykonos flight, often on an A320, deliver you island-side; their business class on this stub includes blocked middle seats and lounge access at Athens' well-regarded Aegean lounge.
My insider tip: fly into Mykonos in the shoulder months of April-May or September-October, when the island's business-class demand collapses but flight frequency hasn't yet been cut — the LHR and FRA connections thin out in winter, so booking mid-season protects your seat choice. Fares on this routing swing dramatically with these hub choices and seasons, so setting up fare alerts for the SFO-JMK corridor is the smartest move before you commit to a ticket.