Rhodes rarely appears on a Midwestern traveler's radar as a business class destination, which is precisely what makes routing through Europe's best carriers so rewarding. There is no nonstop option for business class from Indianapolis to Rhodes, and the reality is that this journey always involves at least one connection, typically through Munich, London, or Athens. Lufthansa's option via Munich is a favorite among frequent flyers on this itinerary: the carrier has been rolling out its new Allegris business class on select long-haul aircraft, though on this routing you're more likely to encounter the reliable, well-configured older business seat on the transatlantic legs, followed by a short intra-European hop into Rhodes. British Airways routes through London Heathrow, where Club Suite—with its sliding door and direct aisle access—has become the gold standard for transatlantic comfort, though the IND–LHR leg from Indianapolis typically operates as economy or premium economy before you upgrade for the long-haul segment onward. Aegean Airlines, Greece's flag carrier, becomes essential for the final approach, connecting through Athens with a comfortable regional business product ideal for the short hop to Rhodes.
My strong recommendation, based on years of booking this exact combination, is to fly Lufthansa or British Airways on the long-haul segment and let Aegean handle the Athens–Rhodes leg separately if needed—this often unlocks better award availability than trying to book the entire itinerary as one carrier's codeshare. Munich has a genuine edge as a connecting hub here: its business class lounges are spacious and rarely crowded compared to Heathrow's Terminal 5 during peak summer congestion, and the airport's efficient transfer process shaves real time off tight connections. Seasonally, April, May, September, and October are the sweet spot—you'll dodge the Aegean high-season crush while still enjoying warm, sailable weather in Rhodes, and airlines tend to release better business class award space during these shoulder months as leisure demand softens.
Given the complexity of this multi-carrier journey and the fluctuating award space across three different alliances, setting up fare and award alerts is genuinely the smartest move a traveler can make before committing to dates.