My wife and I will be in Athen the end of June and are curious on suggestions for 4 days in Athens. Assuming visiting the Acropolis and the sites near Plaka where we will be staying.
With 4 days I wouldn't miss the National Museum. The Ancient Agora is also fun and interesting.
Rather than do a lot of keyboarding or cut-and-pasting, I would refer you (sorry, Rick!) to another travel forum with regular contributors who are actual Athens residents; Their in-depth, up-to-date information is unparalleled. they are not giving you hints based on one trip; they live there every day.
One of them, "Nick_Arch" is an architect who is WIZARD on outlining, step by step, wonderful tours. Just go to Trip Advisor Greece Forum.. go to the "Athens" forum. In the "search" slot put "Athens sights in 4 Days" and also "Athens Sights in 3 days". I guarantee you, there will be at least 50 threads pop up with DETAILED instructions and links!! Please DO use the search factor, because these guys have devoted sometimes hours to spelling out itineraries, and there is no need to ask them to re-keyboard it all. I myself have been to Athens at least 10 times and am always discovering new things, but I defer to Nick and to "Gas" and to other Athenians for their loving knowledge. Happy Hunting!