Hebe (Robin) is looking for alternatives to Herodotus for her Greek classics group. Anyone who blogs about coffee foam and quotes Socrates has to be a nice person, so I gave the question some thought.
I'm guessing the Iliad, the Odyssey, and Thucydides' History of the Peloponnesian War are all too obvious. The group probably did them to death before turning to Herodotus. So assuming they're ruled out, what's next?
Please read Aristophanes. He's hilarious.
Aristophanes, son of Philippus, of the deme Cydathenaus, is one of the greatest comic playwrights of all time. My personal top three list is Aristophanes, Shakespeare, and Spike Milligan. In fact, Aristophanes's work and the Goon Shows bear a striking resemblance to each other.
Most of what he wrote is still very accessible today, though it's true that the more history you know, the more jokes you get. The two best of his plays for a modern reader are Lysistrata, in which the women of Athens go on a sex strike until the men make peace with the Spartans, and The Clouds, which made fun of the philosophers via the Thinking Shop, and starred Socrates as a character. When The Clouds was first played, Socrates stood up amongst the audience so everyone could see who the play was about.
Here's a passage from The Clouds in which a student is teaching Strepsiades about maps.
Student (pointing to a map): Over here we have a map of the entire world. You see there? That's Athens.
Strepsiades: Thats Athens? It can't be, I don't see even a single law court open.
Student: It's quite true, it really is Athens.
Strepsiades: Then where are my neighbors of Kikynna? [a suburb of Athens - Gary]
Student: Here they are, and you see this island squeezed along the coast? That's Euboia.
Strepsiades: Oh I know that! It was Pericles who squeezed it dry. But where's Sparta?
Student: Sparta? Right here.
Strepsiades: THAT'S MUCH TOO CLOSE! Move it further away.
Think about how much you just learnt about Athenian life from those few jokes. You can actually learn more about real life in Classical Greece from a single Aristophanes play than all the tragedies put together.
Despite the lampooning, Socrates and Aristophanes were friends. In the Symposium, Plato has Aristophanes and Socrates hanging out together. One thing that never ceases to amaze me is all these guys who we revere today as world-class geniuses all knew each other. Can you imagine being at a party with this bunch?