Am going with my daughter and 2 teen age granddaughters to Rome next June. When do we book? I have looked at fares from American and Aer Lingus and an online travdel agency. The fares vary widely I prefer no stop and we have two airlines from Chciago that go non stop to Rome,but for a better deal I would make one stop. The AA fare quoted today is outrageous, about $2200 for coach.