Innsbruck's Alpine runway, hemmed by mountains on both sides, is one of Europe's trickiest approaches for large aircraft—which is precisely why nobody flies there nonstop from Southern California, and why the routing you choose matters more than usual. There is no direct business class from San Diego to Innsbruck; every itinerary funnels through a major hub, with Munich and Frankfurt the two gateways that make the most sense given the short hop remaining into Tyrol. Delta and United both offer one-stop connections via their transatlantic gateways (Delta typically through JFK or Atlanta into a European partner hub, United through its Star Alliance network), while Austrian Airlines, as the flag carrier, is the airline I steer most seasoned travelers toward once they've crossed the Atlantic—its Vienna hub connects efficiently onward, and its long-haul business class product, with lie-flat seats on widebody aircraft, is a comfortable way to finish a long journey.
Having routed this trip more times than I can count, my advice is to fly the long transatlantic leg on whichever US carrier gives you the best lie-flat product out of your preferred West Coast gateway, then let Austrian or a Star Alliance partner handle the final continental hop into Innsbruck—that last segment is short enough that seat type matters less than simply landing in daylight, since the mountain approach is far more scenic (and easier to enjoy) when you're not squinting into a sunrise. An insider tip few travelers know: Munich's rail-to-air connection and generous minimum connection times make it a far less stressful transfer point than Frankfurt during winter ski season, when Innsbruck-bound flights fill with equipment and delays cascade quickly.
Ski season (December–February) and midsummer push fares upward, but January, February, March, October, and November consistently offer the best value on this corridor's business cabins, particularly midweek departures avoiding the Friday ski-crowd surge. Given the multi-carrier, multi-hub complexity of this route, setting fare alerts is genuinely the smartest way to catch a well-priced business class seat before it disappears.