Plus the food. :’) I’d want to spend a few months wandering around the Aegean, Greece, and Turkey, preferably in a small group for safety (but everyone would have to be on the same page, no retro-disco-loving freaks who want every night in glitter-ball clubs in Bodrum), but wind up in Italy. There are lots of nice ruins in Sicily and southern Italy, and the Renaissance stuff in Tuscany, and a little of everything in the Piedmont.
When I was at Troy we had a professor of Classics, Dr. Agnew who may have been the smartest person I ever personally knew. He had done just what you want to do and took slides everywhere he went.
I belonged to the Geography Club and we had him one night to tell us about the Aegean, Asia Minor and Crete. He seemed to have spent most of his time on Crete which led to my interest in it.
He had also visited the old Mycenean ruins rather than Athens and the more well known sites. The only thing which bothered me is he would often answer a question with “I don’t know” when I suspected he did know or at least had an idea.
I just spent a couple of years in Italy as an ex-Pat. It gave me a great opportunity to really see the old stuff without being too hurried. I also got to see obscure antiquities off the beaten path....