stepsister's lament - cinderella if momma was married - gypsy i will never leave you - side show my friend - the life marry the man today - guys and dolls
My Own Best Friend - Chicago Baby, Dream Your Dream - Sweet Charity
Both great duets, I don't think other girls would audition with one of these two. They aren't the most popular song from both of those shows, but they are great duets.
I Still Believe - Miss Saigon Three Bedroom House - Bat Boy What You Don't Know About Women - City of Angels I Know Him So Well -Chess
"It's really crazy backstage. Just before the show started, Elaine Stritch got into a fight with stage hand, and then inexplicably started squeezing Hugh Jackman's buttocks. And by the time they had sedated her, she had punched out two cops and was holding Norbert Leo Butz hostage, threatening to kill one of his three names." -Nathan Lane
I LOVE Marry the Man Today. It's one of my favorite tracks on the recording.
If you're going to do sad, lovey-dovey songs (I Still Believe, I Know Him So Well...) In His Eyes might be a good choice. It might be a tad bit overdone than the suggestions that are here, but it's very pretty.
And of course, there's Take Me or Leave Me...
ETA: Forgot to mention, there's a GORGEOUS tune called "The Turtle Dove", and if you're willing to harmonize it, it sounds FANTASTIC. Not a musical theatre piece, however.
This might be a bit too non-theatrical, but you could do "By My Side" from Godspell. Did you know that Stephen Schwartz didn't write that song? It was written by the original actress who sang it in the show.
I second the suggestions for "I Still Believe" (Miss Saigon) and "For Good" (Wicked). Also, I want to suggest "Somethings Are Meant to Be" (Little Women). I thought I had a few more to offer, but my brain stopped mid-post.