I don't envy the people who have to say which of the ancient Greek theatres deserve UNESCO listing because there are a lot and even some of the small ones I've been to are nonetheless impressive. For example, the huge theatre of Epidavros is famous and well known to most Greekophiles but there is also an absolutely charming and much smaller amphitheatre nearby called the Theatre of Palaia Epidavros. 
But I will stick to the script and mention a visit to the aforementioned huge theatre at Epidavros.
And it is indeed, hugely impressive and is still used for concerts even today.
There's also a very nice museum on site with some artifacts that wouldn't be out of place in the national museum in Athens.