Where to fly into is rather limited, esp. if you are committed to a given airline alliance. If you wish to fly direct from the states, you'll end up landing in Milan, Venice, Pisa or Rome. If you change planes someplace in Europe, you can probably get a bit closer to Ravenna (e.g., Bologna, Florence).

Ravenna is an extraordinary city which many people overlook. It has some of the best preserved early Christian and Byzantine art anywhere in the Mediterranean. The Masoleum of Galla Placidia, Church of San Vitale and Church of Sant'Apollinaire in Classe are all worth visits.

W/that said, it probably isn't a place where one would want to spend 10 days.