I don’t really like this itinerary- the destinations are really far apart from each other for such a short trip. Why is Athens a must see? I’d say the ruins, etc. are worth a good day, maybe day and a half, but you don’t need 3 days in Athens. The real reason, IMO, to visit Greece is to visit the islands. I haven’t been to Mykonos, but heard great things, but Santorini is spectacular. It is VERY different “just lying on a beach” in Greece than Florida…there’s no comparison, IMO. There’s also lots to do on the islands.

I haven’t been to Budapest, but have heard great things. With only 12 days, I’d just head to Greece, doing Athens and 2 islands. Or, I guess you could fly into Florence, spend a solid 3 days there, and then fly to Athens, visit an island, and return to Athens and fly home from there.

What are your plans for 2 full days in Athens? IMO, it’s about 1/2 day too long for Athens but nowhere near enough time to actually experience anything about Greece. An extra day is not going to help you make it to any of the islands unless you only see the airport in Athens. An extra day will allow you to take a day trip from Athens — nice if you’re into Greek ruins, but I’m not aware of any great beach options that are easy day trips from Athens.

I’d skip both Budapest and Athens and spend all 12 days in Italy. Although, since you’ve obviously all spent 4 days in Rome before (why else would you skip it?) and are willing to take a couple of flights you could add either Budapest or Athens.

I like Budapest, but 3 full days was enough for me. However, I’m sure I would have found enough to keep me interested for another day if there was a significant difference in flight costs.