I am not aware of any films that make more than a cursory effort at an unbiased, historically accurate portrayal of an ancient Greek setting. Agora (2009) and Alexander (2004) put a modicum of effort into certain kinds of historical accuracy; but they're designed as tendentious pieces, elevating ancient anecdotal gossip above modern evaluations, and warping their material a great deal. That's purely on the historical side of things, not an assessment of filmic quality: I couldn't endure more than 30 minutes of Alexander, but that's a subjective matter.

For historical setting, if I had to choose something, I guess I'd go for Agora, just for the aulos-playing scene. There are a few "peplum" films that may be worth checking out: I haven't seen La battaglia di Maratona (1959), L'assedio di Siracusa (1960), or Il tiranno di Siracusa (1962).

Wikipedia has a list here; another, rather weirdly selected, list here; and for mythological themes there's this list.

I'm not sure what "accurate" would mean in the context of a mythological theme. If you mean "faithful to a specific source", your best bet would be film adaptations of ancient Greek plays: there are many of these. They tend to be rather low-budget affairs with limited appeal. List here.

Edit: I see L'assedio di Siracusa comes with the tagline "Amazing Secret Weapon of Archimedes!", so count that one out for historical accuracy.

Well I do like Roberto Roberto Rossellini´s Socrates. I would recommend taking a look at it since it shows many ancient Greek ceremonies that are not often portrayed due to the often times belicose nature of said films.

http://en.wikipedia.org/wiki/Socrates_(film)

whether its an "accurate" representation of what happened, no one can say, but it does try its very best to be historically accurate and it follows the Platonic dialogues very closely. Its actually a bit sad that it doesnt get to cover such topics as the the second Peloponnesian War in greater detail, but it gives you a sense of why Socrates was executed and how this events where closely tied together (Sparta´s invasion of Athens and Socrate´s trial)

Follow-up (separate post as you'll miss this otherwise): I've consulted with a colleague who is very knowledgeable about depictions of the ancient world in film, and he agrees that Agora is the best bet, by quite a long way.

But he also recommended as the best screen rendition of the Odyssey ever this 1968 Italian TV production (8 episodes) with Bekim Fehmiu and Irene Papas, directed by Franco Rossi. There are bits of it on Youtube, but nowadays it's only available in Italian, with no subtitles. This seems to be a theatrical release version of it. It comes highly recommended enough that I'm planning on watching it anyway.

Edit. The entire TV version of L'Odissea is available on-demand through this Italian website if you have the Hola extension or similar.