Stick with something that suits you and showcases your talent. A tried and true classic whether over-done or not that suits you is better than some random song from a random show that no one has ever heard of that doesn't sound as good. Good point about the piano players. Keep them in mind when choosing an audition piece (stay away from Sondheim).
"When you're a Jet, / You're a Jet all the way, / From your first pirouette / To your last grand jete." --Brian Kaman
Also, I'd recommend to you some Bock and Harnick specifically the title song from 'She Loves Me'. Even 'Suppertime' from CHARLIE BROWN (even though it may be a tad bit overdone, I think).
"I know now that theatre saved my life." - Susan Stroman
You should cater your song(s) based on what show you are auditioning with. Thank you Wonderboy for asking the obvious. This poor person is trying to get ideas and everyone keeps leading the conversation astray...