There's no nonstop path linking Silicon Valley to the Cyclades, which is precisely what makes routing strategy the real art of booking business class from San Jose to Mykonos. The honest answer for anyone researching this journey: expect two connections, since JMK's short runway only accommodates narrow-body regional aircraft, meaning your long-haul comfort happens on the transatlantic leg and you'll transfer onto Aegean Airlines metal for the final hop from Athens. My preferred routing threads through Frankfurt or Munich on Lufthansa, where their newer Allegris business suites (still rolling out fleet-wide, so check aircraft type before booking) offer sliding privacy doors and genuinely restful bedding for the roughly 11-hour Bay Area to Germany segment. British Airways via London is the other strong contender, particularly if you can snag their Club Suite product with direct aisle access on the 777 or A350 out of SFO or a connecting West Coast gateway.
Athens is your critical pivot point regardless of carrier, and this is where seasoned travelers separate themselves: build in a three-to-four hour buffer there, not because of typical delays, but because Aegean's Mykonos flights often shift gates late and the island-bound crowd creates unexpected security bottlenecks in summer. If your schedule allows, consider overnighting in Athens rather than same-day connecting — it transforms an exhausting travel day into a genuine two-city experience, and Aegean's business class, while regional in seating, includes proper meal service and lounge access at ATH that's worth savoring rather than rushing through.
April, May, September, and October reward patient travelers here twice over: shoulder season pricing on the long-haul segments coincides with Mykonos at its most livable, before or after the peak crowds. Award space on Lufthansa's Star Alliance partners tends to open roughly 10-11 months out, then again in last-minute inventory dumps three weeks before departure — a pattern worth tracking rather than guessing at, which is exactly why setting fare alerts for this specific routing pays dividends over manual searching.