Xairete! (Ancient Greek for "Greetings!)
If you're into Nietzsche, you'll probably like the existentialists/absurdists, who were heavily influenced by Nietzsche:
I'd recommend Dostoevsky (particularly Crime and Punishment, and The Brothers Karamazov), Albert Camus (especially The Plague). In a similar vein (the meaninglessness and absurdity of life, etc.), of course read Samuel Beckett's play, Waiting for Godot.
An interesting philosophical novel written during the early '70's by Robert Pirsig, called Zen And The Art of Motorcycle Maintenance, examines eastern philosophical thought (esp. Zen Buddhism) compared to western thought (esp. classical rationalism exemplified by Plato) in a fairly entertaining narrative. Plato comes out the loser for Pirsig, but I'd argue Pirsig's characterization of Platonic philosophy is narrow and somewhat shallow. Still, it's a good introduction to philosophy in general.
As for Plato, certainly don't miss reading his masterpiece, The Republic. Socrates and two brothers, Glaucon and Adeimantus (my avatar namesake lol), build the "perfect city" from scratch in a marathon, all night dialogue. The city that results is not one that most people would choose to live in, a fairly repressive regime, for which Plato has been much criticized by liberals. But those critics fail to recognize that the whole project is tongue-in-cheek; that is, Plato builds a political system built strictly on reason in order to demonstrate the LIMITS of reason.