I'd like to visit Trieste, Italy, specifically, ICTP-International Center for Theoretical Physics because this is where my most admired university professor took his Masters. He's simply amazing. Well, there are lots of beautiful place I'd go after. =)
I would love to go to Rome. My mother-in-law was there last year and the pictures she brought back were amazing. The ruins, the history, Vatican City, the museums. There is so much to see that I know I could spend weeks there.