Is it a strict ballroom dancing class, or are you teaching swing as well? If so, most of the young people around here will do swing to any of the older tunes or contemporary music. If you are teaching Quick Step, the popular tune "Hey Soul Sister" by Train works for that dance.
Some more current country music is usually OK for some waltzes. And I think I would agree about the cha-cha for the Lady Gaga tunes.
Otherwise, I am not well-versed on what kids are really listening to these days. It's possible that if Miley Cyrus slows things down a bit on a ballad, there might be a slow Fox Trot hiding in there someplace.
The Dancing with the Stars website used to post the songs that the couples did routines to, but I am not sure it still does. If so, you can always find some current music that was used for Tango, Paso and Rumba on that site.