Assuming you can't (or don't want to) sing something from the show at your audition, you might consider something from another Adler-Ross musical from the same era, DAMN YANKEES. There are a few good romantic songs for men: "Goodbye Old Girl," "A Man Doesn't Know," and "Near To You." I think a couple of those might be M/F duets but could easily be arranged as a solo.
"Word of advice: Be who you are, wear what you want---just learn how to run real fast." Marc, UGLY BETTY