How long have you got? If you are coming over from the states, then probably the longer the better.
My favourite stop in this trip was Dubrovnik, a really beautiful place with so much history. Lovely people and amazing food.
In Italy I have only been a few places but Venice is again an amazing sight to see, though very expensive. Lake Como is just breathtaking and Milan if your want some city life.
I now live in France near the boarder with Switzerland and highly recommend this area if you want some mountain adventures. But of course that is what made me move here, so I am a little bias. Chamonix is pretty special as it sits at the bottom of western Europes biggest mountain Mont Blanc the views will just make your jaw drop. Or Morzine is great place if you want to mountain bike.
I'm sure no matter what you choose you will have an amazing time.