Roger Crowley's excellent book City of Fortune covers this -- both Genoa and Venice established trading houses and ports at points on the Black Sea. Caffa itself was purchased from the Golden Horde in the 13th century by the Genoese to act as a hub for Eastern trade to be picked up and shipped back to Europe/other markets.

It is significantly easier to ferry goods over water than over land (especially around bodies of water like the Black Sea) when you have the ships to do so -- and Genoa (as a merchant republic) most certainly had ships. Having a port in the black sea meant they could get as close to the overland trade coming in from the East as possible.