If I don't want to fly to Italy what are my options via a cruise?

There are repositioning cruises in the spring when they transfer ships from the Caribbean to the Mediterranean. They can be some pretty good deals that friends have used. But you might have to wait until fall to return and dance around the Schengen limits.

Search the Cunard website. I have been getting email offers for some of their cruises.
I believe they have a crossing from Ft. Lauderdale to Italy.
Search Transatlantic Crossings on their website.

Look at vacationstogo.com and input transatlantic. Many of the cruise lines will pop up - just search the month you want to go.

It gives you a quick itinerary search without pulling up each and every possible cruise line. Just know that some cruise lines may not be reflected, like Windstar or Ponant.

Ah, there is something mesmerizing about a transatlantic voyage. Cunard at least, makes a point to state that this is a voyage and not a cruise. Many years ago, I took four transatlantic voyages. They were awesome. I would so it again in a heartbeat but be prepared for some incredibly rough seas in the North Atlantic. There were 20-30 ft swells on on crossing. Other days, the ocean was as smooth as glass. I would sit for hours on the covered observation deck just watching the ocean. No jet lag was also a plus.

Last I checked Cunard is the only one who crosses regularly in both directions. The other lines just reposition - eastbound in the spring and west in the fall.

Cunard travels between NY & Southampton - you will have to make the rest of the journey to Italy by other means. Very few...if any end the crossing in Italy without several port calls in Europe.

There are one or two scheduled Cunard QM2 transatlantic crossings that have a port stop in Le Havre, France, or Hamburg, so either of those may work for you. As for the "incredibly rough seas" mentioned in a post above, the QM2 manages them beautifully and they are encountered mostly in the late or very early season crossings.

We have taken a few transatlantics, all spring repositioning cruises. I also like to start with vacationstogo.com for the big picture, then book directly with the cruiseline. They can be a great value. I would also suggest you consult the cruiseline about their air....some great deals possible when you purchase air through them. Our most recent experiences--- $850 pp balcony 14 day crossing, rountrip air $650 pp. One was to Barcelona, the other to Rome. We had 30 days from disembark until we had to fly home, and other departure cities ( not just the port of disembark) are possibilities. Also, the insurance from the cruiseline covered our entire independent land travel. These prices did not include taxes and tips. These have all been on Holland America. About 10 days ago I saw a Holland America cruise, 14 day transatlantic departing 30 March for $699 balcony pp. the cheapest I have ever seen, this was the Westerdam, Ft Lauderdale to Rome. Ocean view and interiors may be even less but I look only at balcony fares. Good luck. Hope it works out. And cruisetransatlantic.com might also be helpful for "big picture" overviews.

Norma, my experiences were with fall crossing on the QE2. Yes, the seas were rough but despite my having issues with motion sickness, I never suffered from sea sickness on these voyages. The ships are designed to handle the seas. I am not so sure this would be the case with a ship NOT designed for the crossing (eg re-positioning cruises). Many years ago I was on a Cunard ship sailing up the east coast from Florida to Quebec City. We hit the tail end of a hurricane. I was sick as a dog. But this ship was not designed for transatlantic crossing per se.
I was also on the QE2 NYC to Southampton voyage shortly after the ship ran into the "perfect storm" of movie legend. There was a visible bend in one of the steel planks on the bow. The captain explained how a" watcher" saw a massive swell approaching. They were able to turn the ship so the bow faced the swell, causing the bend. If the ship had been caught broadside, the captain stated they would have floundered.
So, if I was to cross the Atlantic on a ship, I would want to be in one that can withstand whatever the sea may throw at it and the crew at any time of year, be that a cargo ship or a cruise ship.