Well, Dr. Awkward is right about Centaurs in Greek Mythology. Yet Chiron was notable for his ability to heal. Similarly, I used one satyr as an oracle. You can use any element of Greek Mythology with satyrs, and it will seem right.
Create an Enkidu-like Satyr, rampaging through the countryside, and give him the gift of the Nemedian Lion (DR 20/Bludgeoning) and have the PCs track him. Encounter seems right. Have the satyrs play the part of mythological harpies, befouling a king's food as a punishment from the gods. Hey, it could work. There are tons of Greek stories that you could use, swapping satyrs in for other characters, that would work just as well.
Go further afield, and have a satyr play Cyrano de Bergerac to a PC Roxane or Christian de Neuvillette.
Or just say, "Satyrs represent wild nature, abandon, revel, delight, and panic." Then imagine what satyrs are like who represent a huricane, or a storm. Throw in the proper setting elements, use some templates, and Hey Presto! you have a cool satyr encounter that has little to do with sex. Satyrs that are as liable to tear you to pieces as to waggle their nether parts at you could make a good encounter.
Seriously, imagine this scene: There is a storm brewing. The PCs are in the forest, hunting something nasty. Of course, they are going to just hunker down and wait out the storm, then continue the hunt when it has passed. But the satyrs pipe to panic them, and in their fear they flee willy-nilly into the woods, facing hazards of wilderness and storm, and having all sorts of fun encounters while the storm rages. And then, with the storm passed, they discover that what they once were hunting is now hunting them, and they are no longer together......
Or just say, "Satyrs represent the what comes of the grape, for good or ill" and play them like drunks, some very forward (but not necessarily very capable at the moment), others bringing comfort, and still others leading PCs to do things that inhibition would normally prevent them from doing (which may or may not be sexual, but could be great fun for the PCs if they can tweak the Duke's nose and get away with it by blaming the satyrs).
You could play up the devilish look of satyrs, and make them great tempters of mortals.
Like most monsters, satyrs can be used in many ways, and still retain their primary "satyr" qualities.