You can find these flights on Google. If you want to travel in August, you can get from San Francisco to Milan for as little as 542$ roundtrip on Star Alliance and as little as 608$ SkyTeam. (*On September 10, 2024, you can fly from San Francisco to Milan roundtrip for as little as $508 on Star Alliance.) There are many great dates in October flying Chicago to Milan and in September you can fly on Star Alliance to from NYC to Milan from as little as 452$ roundtrip.
LINK to sample Google flight: https://www.google.com/travel/flights/s/872HX2f7n7p9wJCEA
Milan is a modern, clean airport to fly into. If you want to rent a car, exploring the Northern Italy towns like Bergamo or Verona or Lake Maggiore or Lake Como are a must.