I don’t see anything wrong with your original plan, Naples, Rome and Florence. You have said that you don’t want to rent a car and it doesn’t sound like Venice is a must-see, since you have already been there once. I’m with you on that. I went there once for one day, took the train from Padua. Glad I went, don’t particularly want to back though a week there without tourists would be great. You can travel locally from all those places if you wish and two weeks is a good amount of time to split between three places (four if you include Milan). I will suggest one other place for you to think about, Malta. Lots of history including some very ancient, very easy to get around by bus, good beaches, good food. It’s a good place for a very laid back vacation for someone from the USA. You would have to fly there from some other large city so you could plan something like go to Paris, London or Rome for a couple days, fly to Malta, return via a different city. Wherever you go, just don’t try to cram too much in, go somewhere and allow enough time to enjoy where you went, rather than rushing from place to place just to say you have been.