Cork's compact terminal has quietly become one of the more civilized entry points to Ireland, and reaching it up front from Ohio requires a bit of strategic routing since there's no nonstop option. Business class from Cleveland to Cork means connecting through a major East Coast or European hub, with United via Newark or Dulles, Delta via JFK or Atlanta, and American via Philadelphia or Chicago all offering one-stop itineraries into a partner or joint-venture European gateway before the final hop to Cork. Total journey time typically runs well beyond the route's nominal 7-hour flying time once you account for the connection, but the payoff is a lie-flat experience for the long transatlantic leg — United's Polaris seat, Delta One (increasingly the suite version on widebody aircraft), or American's Flagship Business on their 777s and 787s all deliver direct-aisle-access seating that makes a red-eye into Europe genuinely restful.
Having routed through Dublin and Shannon myself before catching a puddle-jumper or a rental car down to Cork, I'd steer seasoned travelers toward positioning through Dublin when possible — immigration pre-clearance for the US is available there, but more importantly, ground transport onward to Cork (roughly a 2.5-hour drive or a quick regional flight) is far more reliable than connecting through smaller UK airports in shoulder season fog. My insider tip: build in a same-day buffer if your final segment into Cork is on a regional carrier, since Irish coastal weather in autumn and winter can cause delays that don't show up in typical on-time performance stats for the mainline carriers.
January through March and again in October and November are consistently the softest months for premium fares on this corridor, largely because Ireland's tourist surge hasn't yet hit and business travel demand from Cleveland's manufacturing and healthcare sectors dips slightly. Given how much itinerary construction (and pricing) can shift week to week across three competing US carriers and their European partners, setting up fare alerts for this specific city pair is the smartest way to catch a premium seat before it's gone.