Italy 4 nights / Greece 4 nights

With the 'givens' you present, you definitely need to plan to fly an 'open jaw' routing. (US-Rome-Athens-US or US-Athens-Rome-US)

I would vote to stay all the nights in one place in each city. You do not have the time to be moving out of & into hotels multiple times.

A day trip to Hydra from Athens may be something to consider to get your 'Greek Isle' experience on such a short trip

With only four nights for each, I would stay in Rome and Athens. You don't have time for more than that.

Thank you
Looking at Hydra for a day trip.

I agree with spending 4 nights in Rome, I did not find Athens as charming nor as many sites to see there, so maybe 1 or 2 nights somewhere interesting and close. For a day trip I really enjoyed Aegina, a one hour 15 min ferry from Athens’ harbor (Piraeus). Lovely place to swim, not crowded when I was there in early September. Enjoy!

Athens is worth 3 nights for me. However to visit any other place you need more days than just 4 nights therefore stay put in Athens for the 4th night.

Rome is good for 4 nights.

Your itinerary:
US - Athens - Rome - US

I've never considered Athens to be more than a full day of touring the sites in the city itself. But this is all subjective. I also agree that you should make this a multi-city flight. Land in one, leave in another.

If you are interested in ancient sights, you will easily fill 3 full days in Athens. If not, you may want to take 1 night away and add it to Rome. There is definitely a lot more to see and do in Rome.

Hi,
I would recommend visiting Thessaloniki in Greece. It has wonderful architecture it is easily accessible by train, car or plane. The food is excellent and the people are friendly!

There are definitely enough ancient sites for 4 days in Athens. Someone suggested a side trip to Thessaloniki - we spent a week there. To try to fit it in to a total of 4 days including Athens is too aggressive. You will just be frustrated. The island of Hydra is beautiful (no motorized transportation - donkeys and shoe leather only) for a day trip as is Aegina. There is a 3-island itinerary that includes both of those islands as well as Poros. You will not be at each of the islands long enough to enjoy them if you make this your selection. We used Rick Steves pocket Athens. If you haven't already, get it. BTW - everyone everywhere in Greece speaks English so don't have a concern about "it's all Greek to me"!

That hop from Rome to Athens is going to eat up a good portion of a day so you have just reduced your effective touring time to 7 and a half days. When you add the effects of jet lag after a transatlantic trip that first day after arrival can be a bit of a difficult one until your systems come into alignment with local time. I said all that to suggest that you choose one of these destinations and concentrate on getting the most out that one place and not waste time hopping. As others have indicated Athens can be done nicely in 2 or three days however Rome has so much to offer and requires more time. We have spent 12 days in Rome and really only saw the highlights.
I would choose to just stay in Rome.
Here is why.
Rome http://www.flickr.com/photos/stanbr54/sets/72157634677664021/

Return to Rome https://www.flickr.com/photos/stanbr54/albums/72157661593187885

If you really are set on doing both I can assure you that you are not going to be able to see all this in 4 days in Athens.
Athens http://www.flickr.com/photos/stanbr54/sets/72157632121475515/