My suggestion, if you want to save money, is join the Alaska Airlines Mileage Plan. I use miles on them every year to fly from Portland to Europe, on partner airlines. These days, you'd probably fly AA on a partner award. Alaska's program is flexible, and I think you'll find good availability next spring to Italy. (No cost to make seat assignments on award tickets. Also, free changes/cancellation up to 60 days before departure.) Try it yourself: you can search for flights using miles on Alaska's website and see what's available now for April-May. I just did and found a bunch of flights for 20K miles each way with one connection (Miami, Charlotte or Philadelphia) between MSY and Milan or Rome. You can book an open jaw: into Rome, out of Milan or vice-versa.
OK - but how to get miles by next spring, you ask? Credit card miles. Alaska has a good partnership with Bank of America. You can get 30,000 miles just for signing up for a card and spending $1,000 in the first three months. The card normally comes with a $75 annual fee (not waived the first year)...BUT, there's a trick to get a $100 credit after you spend that $1,000, in addition to the 30,000 miles. (Easy to find the $100 sign-up link by Googling.)
That's 31,000 miles. If you happen to spend a lot on credit cards, you can get $1 per mile and get the rest of the miles you need pretty quickly. Sometimes Alaska puts their miles "on sale" if you need to buy enough to get the amount you need for the next ticket.
OR, believe it or not, they will let you get more than one of these credit cards at a time! I think you have to wait 90 days - but I have done it. They don't seem to care. (When I called to cancel one of them recently, the agent said, "Oh, you don't need the other companion pass anymore huh?" I guess people get two cards at once - and get the bonus for each - so they can get companion passes for their families - not something I need.) And, you can cancel before the year is up (to avoid the next annual fee) and sign up for a new card - and get the bonus again. Again, they seem to allow it.
Yes, if you get too many credit cards, you may affect your credit rating. And I'm assuming you would pay off your balance every month and not run up big finance charges. Not sure if that maters to you or not. But I've appreciated getting a round-trip ticket to Europe for almost free (about $100 in airport fees/service fees per ticket) the last several years in a row.
Maybe it's too late for you for spring of 2018 to get enough miles for a round-trip ticket; the 20K one-ways may be gone by the time you get enough miles to book. But if you want to go again in 2019, best to start now. If you have United miles too, you can sort of combine them: Alaska lets you book one-way tickets for half the miles. Maybe United does too? If you can manage to find a good one-way United award flight, at least, you could book the other way's flight with Alaska miles.